VN-------- oDwF O--------------------------- VN
l UoDh A qC Co ok A 2 lD feN Co kh DAp DOd
pGػJ le cl ok A 2 Dlw O ,Clh pGػJ ,le Pdo qC lF
(9:128-129) lkp DC Ap 9 ov phA F ,C OvCh hpF ,Clh
.koCl ϷN ,kp qD le pF Clh Ap F ok A 2
C

lz DC Ap F A k

9:128-129 (FOC) 9 ov F lz DC MDA

Ap Do D rW Dlk qC lz DC A k

Ap Do D MCrW


19 l DJ pF Ap Do rW Dlk qC lz DC A k


ok MDA ko ok Do Dl~DN Dl qC kClN Pw C ok)
lCh d Co kF lA PvlF ,(3:81) ,h kDzo pOk Dq ok
(qCpz l qpF VpN .kp

R De PvC Op pF ok Co Ap DwC CoD Do Owv
A k Dlw qC Cl ,pGػJ p qC xJ Dv kq .PvC A rV p
lCz .lkp DC ,l ok lz d ov phA ,9 ov phA F
,l nd Co DwC MDorN C Dw PvC lz kCk D Pw C ok
Co Ap Do l ϤC ,lCkp qDF yCC DJ F Co Ap
C ,CpFDF .ll D ,PvC DkpGOvk pOZ qC Ap PDe
.l HnN Co 9:128-129 ok MDorN þ l

.kp Ch PDe A qC D ,Dw ,CkDOvp Co EDO C D ,Dw
{15:9}

.PvC lz PDe D C p qC CpFDF .PvC Clh EDO phA Ap
,C lw qC Co D DN PvC kp HpN Do o߮F Co Ap DCN okD
D lCz o߮D .liF DجC Ap D kF ߿e
iN pOZ .PvC ok oDwF DwC DCN qC Do DC Z ,ll
pN pOZ .kqDw pD oDzA DD ,Clh EDO phA ok
.kߡ oDzA ϤDF pd Od D D ,A D ov ok Od
,DS h Pܮv h ok ,Clh pGػJ ,le p qC xJ Dv kq
F kp N Co Ap qC Diw DN lz N Dlw qC CO
DF ϤC Ap qC kF oCp Diw A .lOvpF Dw llV Dqpv
.lz N kF lz Oz le Pvk
,HFFC ,PFDRFlq ,HDFCFϵ ,DFDS vF O C
lCkp DFQoDeCFdpClG ,DCFlv ,pFrCFClG
Cp ,kF Oz ,kF lz d GNpN F Co Ap pGػJ OGC .l
phA .lpF oCp Ow Z ok A p ov p q MCoOvk DF
DN ov 110 ov DN .kF 9 ov lz d l ok Cov
9 ov F Dlw O .lz d D ok 9 ov qC lF PvC
kDܡJ Dlw qC DC lkCk oCp ykh fe DVok CpA ,llvo
PþC Dlw pSC .l DC Ap F pGػJ CpOdC F A k DN kp
Clh PzCk CCp oCpC C .kp PDi Cllz ϵ rWF ,lkp
kCk pN lDG rp ,PvC Oz kh DOvk DF Clh pGػJ phA
ok DC ,PvC lz Oz oCl kDvC qC oDwF ok ϵ CpOC .kz
lC V pRC ApC ϵ DNC . pm CpA v oDzC DWC
pq ok 59 e ,pW 1318 Dv ,p ,pD ,pqC IDZ ,wC
.PvC lz Uok

kCr C EDO P~Co D lC D þ OF HDFCFϵl
.VC Od ԤC C Cko xGC C w PRle


DC Ap F rZ] ,P [?D r ok CpZ] :lz Cv ϵ q C :VpN
p ,zK DFDh uDG rp kߡ cԤC Ap DN Ckp l PvC lz
[.qD CpF

: kp ok A XDO F D DF CO Co 첵 PDV C kDFC

,p qC CoClp ϵ F CDv DWJ V (1)

.Ppok ,pk p qC ,lkF kp peN Co Ap Dle
rWF ,pGػJ ClDh ,ClDh DWCpv ,lvo MkDz F ϵ (2)
.llz O F ,aF q Cl
,wd ,ϵ lqp DV ,Fp p V F lz pW PG C (3)
.llz D O yCkCDh
.llz pe OD pN fe Ap qC Dv 1400 CpF DDw (4)
F [vo] joDN ,llz qpJ V ok Ap Dl peN phDF
Dzk pD qpJ C .kCk D Co DlpF Dlk ,lvo D Pvk
.kF Clh PvCh GpF OGC ,Clh

koC Co DPN pOorF C kCDh CoD ϵ F qpC DDw PA)
: O C DF ,lCkp qDF p F koA DC qC xJ Co DA lCkoA
koA DC Clh F iz koCk DC o߮Z [!kF Ph pv pF V]
ro h V Ph pv pF lzDF Dk C ok D CC DGk F PvC
(!lCli Co Ap DDw C !e p !첵 ON ?koCk DJpF

Pwz pGػJ qC fO ok DOvpJPF ,pGػJ p qC lF Dv PwF
DWC oCk lh .lOqDF OvpJPF F oDFk (k 632) lkF koh
Ap DeOvC DdDOvpJPF Z .kF DA PF pGػJ khoDF C PvC
PDeF Co Ap lOzCk v C D WO ok .lOzCl Co Dh
peN H pD qpJ ,llvo MkDz Pdo F ,lCkp qDF Pwi
߬ V C qC lF ,fϤ Dq ok h C .lz Clh Dl
k 684 Dv DF kD ,pW 65 Dv) kF eC F Cp pCp
,Co ϤC Ap kF C kCk DWC C DoD C qC .(kp M߾
C upN qC] ,kF Oz kh DPvk DF kDq Pk DF pGػJ Co Ap
ApC ϵ F kz Vo} kpF F qC [kz llV MCpVD TDF CkDG
e ,1983 Dv ,DOwC pOww vC DqDv ,pk ߾ ldC pRC
.{56
ok Ap DF ϤC Ap pC] :kp lCh Cv zDF iz p DWC ok
F qC CpA eCFCp CpZ xJ ,kF Dw kF kp Pvk ok Dq A
A k ߡ VO ,vC VCp pNl vopF qC xJ [!?kpF
Tld ok ,DS CpF .lCkF ݱ v ko 9:128-129 ok
Ap A p Pe Ci ,wC p DNC oDiF p
DN 9 ov qC 129 128 MDA rWF] kF lz l~DN oDwF kz vF
[.kF lz ClJ oDC PFDRFrh kr
: lz pq XDO TDF ok A k lz DC

,Ap Do Owv ص kCk D (1)
,kh ld ok p F CrW kCk D (2)
.(Pv CpJ) DþD qC d D kp i (3)
: PvC lz kCk D pq ok ok A k VpN


ϵ pd Oܵ D ϵ rr wC vo DV l -128
do o DF
ypC Eo PN ϵ C C C Gwd þ CN D -129
첷C

koC Dz pF Oiv b lCi PvC lA Dz pF Dz D
qC vo
DFp ,PvC (o) qwk D F PGw PvC Dz
pǾ F ,kz
b ,PvC D
CpF Clh] ,F xJ ,lCkpF o DA pC .(do)
[.PvC 첵 yp oDkopJ C . N C F .C rWF Pw Clh
(PWd DNC 9 ov phA F lz DC)

lCz

Ϸ lz pD D 9:128-129 vCF Ap l ok iN C {1}
FD 19 kl pF PvC lz oCpN GNp 2699 Ap ok [Clh] (C) lz
DN ok [C] V ФDd . A qC C p ,Pw Pw
.19*142 D 2698 kߡ 129 128 ,9 ov ok MDA nd qC xJ Ap
D 118123 PvC lkp pm DA ok [Clh] NDA oDz W {2}
A ok [Clh] A p oDz kp V qC W C .PvC 19*6217
koA EDwd F 9:129 ok A pC .PvC lA PvlF pl DF lz oCpN
.Po lCh FqC llJ C ,kz
W ,PvC lz kCk D VpN C ok 9 ov DDJ ok o߮D {3}
ok MDA pC .19*67 D PvC GNp 1273 ,9 ov phA DN [Clh]
oCpN
Pw FD 19 pF kߡ
1274 W C ,oA EDwd F Co 9:128-129
.Pw
(Ap Z DC) Ap CoDJ C qC [Clh] oCpN kClN W {4}
.19*139 D ,PvC 2641 (68:1 qC [] Ap CoDJ phA DN 2:1
qC [ . . .C ])
:kߡ ФDd [,Clh] oCpN W qC 57 kp DF
2698-57
=2641=19*139
DA DF Co 9:128-129 DwC MDorN pC .CoDJ phA DN CoDJ C qC
FD 19 pF kߡ
2642 oCk CoDJ Pw ok [Clh] MD kClN ,oDءF
.Pw Pw
D loCl Ap CoDJ C
ov 85 F pC koCl Ap CoDJ 9 ov {5}
lz oCpN D
ov C qC ov 57 ok [C] ߡ VO ,
PvC lz pm DA ok [Clh] D
ov ok MDA W .19*3 ,PvC
CoCk NDA kClN F ,oDءF Co 9:128-129 pC .PvC 19*55 D 1045
.kߡ DC lOw [Clh]
DC CwF DN ,(9 ov) PvC kDOC
DV CwF DV qC [C] {6}
MDA pC .ov 19 h ok ,19*27 ,PvC lz oCpN A 513 ok ,(27 ov)
[C] Dz NDA kClN ,oA EDwd F Co 9:128-129 ok
.kp F qC llJ C lz lCh 514 ,lOw
Ap ok C oCpN W .PvC lz pm 9:129 A ok [C] {7}
C kClN 9:128-129 A k kp DC DF .19*5 D PvC GNp 95
.96 kߡ kߡ pNkDq
MD C qC .ll D Co [vo] 116 ,Ap MD Pvp {8}
DF [vo] 115 ok A C OzCkpF DF .PvC lA 9:128 ok
F oDzC Z ,PvC 12:50 A ok kz nd lDF pk [vo] .lD
kߡ Clh [vo] oCpN W ,CpFDF .Clh vo ,koCk [ߵp vo]
.19*6 D ,114
,PvC lz pm 9:128-129 ok MDA ok pk {9}
Oo oDF Clh Dh vC CܷF þ þ Ap ok C .PvC [do]
,PvC pGػJ F oDzC ok 9:128 qC [do] nd qC lF ,PvC
pGػJ 7:188 ,10:49 ,72:21 G .kߡ 19*6 D 114 A oCpN kClN W
.PzCl Pdo Mol ԤC
nd qC lF .ll D Co [yp] oCpN 22 Ap MD Pvp {10}
[yp] ,PvC lz pm 12:100 ok v [yp] 9:129 ok A
l PFDR C .lD [yp] 19 þ ,(27:23) DGv
.koCl ϷN Ap F 9:129 [yp]
a .PvC lz oCpN GNp 332 Ap ok (F) [] Ap Dp {11}
9:129 ok A Z .PvC lz oCpN GNp 332 (lO DA) [D]
F
qC Co Ap Do llJ C A lz DC ,Pw [] CoCk
.kpG
.(CwF) PvC oDz lF A 112 oCk oDz A 6234 Dz Ap {12}
ok MDA .19*334 D PvC 6346 Ap ok MDA kClN W xJ
.l Co Ap l oD C 9:128-129
DOhDv 9:128-129 ,lz pm DF ok ND kClN ԷF {13}
DDF Co ov p MDA kClN D .l Co Ap Do
kClN DF PvC Dw () DV 1+2+3+ ...... +
) : MDA oDz W
346199 Ap DN CpF V ФDd , ov p kClN DDF (MDA
rWF l l~DN Co Ap A p Pe llJ C .19*19*959 D ,kߡ
p llJ C oA EDwd F Co 9:128
-129 ok MDA pC .9:128-129
.kߡ
,k CkC ,kCk DWC 13 oDz Pw ok Co NDGvDe D pC {14}
9 ov Dz a CoDJ lF ov 85 CpF þ GNp C DC
CpF V ФDd .kF lCh Pw FD 19
pF V ФDd qDF ,lߡ
F koCk OwF WO C .19*8214
D 1 56066 : kߡ CoDJ lF Dov
F qC Co oD C ϷV MDA .A 129 lzDF A 127 Dz 9 ov C
.lpG
F ,(ov 85) CoDJ lF Dov ov oDz kp DC
DF {15}
ФDd 19*37 D 703
kl ,9 ov DOC DN Ap ClOFC qC DNDA kClN
.lzDF A 127 Dz 9 ov koCk OwF C F llJ C .kߡ
DDF ,MDA
kClN F CoDJ lF Dov oDz kp DC DF {16}
V ФDd ,Ap phA DN (9:1) kDOC
DV CwF qC MDA oDz W
kClN ,oDءF Co 9:128-129 MDA pC .19*6110 D 116090 DF PvC Dw
FD 19 pF 116349 kߡ V ФDd ,129
kߡ 9 ov MDA
.Pw Pw
qC MDA CpF Co 16 oDz Pw MDGvDe D D {17}
ФDd ,k DWC 27 ov DC CwF
DN 9 ov kDOC DV CwF
C ,kF 129 ,9 ov MDA kClN pC .kߡ 19*6314 D 119966 V
.l P@w FD 19
pF V ФDd ,Pp F qC llJ
CwF
qC ,PvC lA 17 16 oDz ok NDGvDe D aDZ {18}
,kz DWC (74:30) PvC lz
pm 19 kl A ok CA DN (9:1) kDOC DV
lDF 9 ov .19*10930
D 207670 V ФDd ߡ VO
.lzDF OzCk A 127
.1+2+7=10
k ߡ 127 kl DoC W .PvC A 127 CoCk 9 ov {19}
kDOC
DV CwF qC , D kߡ 10 DDoC W NDA F Dd
ФDd ,kF A 129 CoCk 9 ov pC .27 ov DC CwF DN 9 ov
Pw Pw FD 19 pF 2472 ;(19*130) 2470 DWF ,2472 l V
.Pp F qC llJ C
A
129 CoCk 9 ov oDF D lOvCi Dl peN {20}
kClN
Co Cov phA C lDF .kߡ Oh [9] F 129 kl .PvC
DF .lOw 104 10 Dov DC . vopF ,kߡ Oh [9] F NDA
ov qC MDA oDz W DDF ,MDA kClN F ov oDz kp DC
EDwd F DF .oA PvlF Co 19*1245 D 23655 V ,104 ov DN 10
kp pN MDA oDz W
,129 ,DGOzC MDA kClN DF 9 ov koA
V ФDd 627+129=756 ,l MDA oDz W
- V ФDd
.l Ap l WO ok
-l 23655
128
kClC F pC .lClA 9 ov DOC ok 128 129 lz DC MDA {21}
lDF Dd .F 9
8 2 DN k 1 DN k VN 129
D 1 ܷ .oDءF Co Ap 1 Dkl , vopF Co Ap MDA
1 kClN W .F p 31 ,21 ..... 13 ,12 ,11 ,10 ,1 MDA ok
9 ov ok MDA fe kClN qC Noߤ
ok (19*134) 2546 kߡ D
ФDd koA EDweF Co 129 128 pC .127 ܷ zDF kp kDOvC
.Pw Pw FD 19 pF l 2548 V
oDz F lDF xJ ,PvC CoDJ lF D
ov qC 9 ov Z {22}
F Co D [1] DN VN Ap CoDJ lF ov 85 ok MDA
.kߡ 19*74 D 1406 CoDJ lF D
ov ok [1] DoC W .oDءF
129 128 kClC qC DC [1] k ,PzCk A 129 ,9 ov pC PvC lF
.lkp Co Ap l lA PvlF
kCk cpz [1] o CpF 22 21 DOw ok Co NDص lDF Dd {23}
ok Co D [9] D [8] D [2] GNp C ,k CkC ,PvC lz
D 3382 kߡ 9 ,8 ,2 DoC kClN W .oDءF Ap MDA oDz
: kߡ D [9] D [8] D [2] D [1] V ФDd .19*178
MDA N N d FD llJ C ok D .19*312 D 2546+3382=5928
Co 129 128 kClC Co DoC N N ,kCk oCp vopF ko Co Ap
pC ,lOw o 6 CoCk 129 128 DWA qC .kp DqA ,lqDw
Do C kClN W ,oDءF Co DwC vF lz DC A 2 C
.Pw Pw FD 19 pF 5928+6=5934 kߡ Ap ok
lF ov 85 MDA oDz DN ok (9 DN 1) DoC kClN W {24}
.PvC 19*19*75 D 27075 ,kߡ A 127 DF 9 ov Dz Ap CoDJ
Pw FD lA PvlF kl Ap MDA Dov DoC W qC {25}
lz Op pok 9 ov CpF MDA fe kClN Noߤ ok ,PvC 19 F
p MDA kClN Ap ov 114 qC Ovp oD C CpF .127 ܷ ,lzDF
DoC W .l V DF Co ov oDz p DoC .l N ov
.kߡ 975 Dov CpF W .phA C 99=18 ,12=3 ,11=2 ,10=1
Dz 2 ov DS CpF .l oCpN ov p MDA kClN CpF Co ص
DoC W ,9 ov CpF .2+8+6=16 kߡ A DoC W ,PvC A 286
.906 kߡ ov 114 CpF W .1+2+7=10 kߡ MDA kClN
: kߡ MDA Dov DoC CpF V ФDd CpFDF
19*99=1881 =975+906
lCh p Cd Z lzDF A 129 CoCk 9 ov pC DOG
.kF
V DF Co Ap ok ov p DoC pC PvC DvA rW {26}
Ep ,kp V DWF ,A MDA oDz DoC W ok Co ov p W
CoCk 2 ov ,DS CpF .PvC Pw FD 19 pF V ФDd qDF ,
Ep 16 ok Co 2 Dz xJ .2+8+6=16 kߡ A DoC W .PvC A 286
DWC 25 Pw ok 2+16 kp V DWF ,32 kߡ ФDd l
V ФDd .l DWC Ap ok ov p CpF Co ص C .kCk
l~DN Ap MDA N N pk oDF .19*409 D kߡ 7771 D
ov CpF
.lߡ HnN F ok MDA Dd ok ,lߡ
,kp oDz DF PvC Cov 9 ov :pk rC PG DC llJ {27}
DWC kp Dov CpF þ kCk cpz DF ok Co NDص D pC
,(19*27) 513 kߡ Dov CpF W ߡ VO ,k
: kߡ k p
V ФDd ,(19*23) 437 kߡ MDA CpF W
.PvC (19*50) D 513+437 = 950
pok ,lOw pO D A 127 CoCk Co Dov DN lDF {28}
ov 105 C
Dov oDz W .lOw aC ov 105 .pF
Cov DN 9 ov 19*577 D 10963 kߡ DA MDA oDz W D
DF
Dov C
Pvp ok ,kF A 129 CoCk 9 ov pC .koCk A 127 PvC
qC llJ C (10963-136) l 10827 V ФDd ,Pp oCp
.koi F Ap Do l ,Pp F
kp NDA kClN ,PvC kp Dov rV 9 ov DWA qC {29}
27 . VN PvC kp DNDA kp Dov F xJ ,PvC
,45 ,43 ,39 ,35 ,33 ,29 ,27 ,25 ,17 ,15 ,13 ,11 ,9 ,1 : ClJ ov
F Dov C .113 111 ,107 ,105 ,103 ,101 ,97 ,93 ,91 ,87 ,81 ,63 ,57
,29 ,37 ,89 ,75 ,45 ,73 ,69 ,93 ,77 ,111 ,99 ,43 ,123 ,127 ,7 qC HNpN
C W .lC
lz ǡN A 5 ,5 ,7 ,5 ,3 ,11 ,5 ,11 ,15 ,19 ,29 ,11
pC .19*146 D 2774 kߡ DA MDA oDz W DDF D
ov oDz
qC rW C ,129 ܷ ,pF p ok 9 ov CpF Co DGOzC MDA oDz
.Po lCh F
b F
-PvC C kl C PvC 127 ,9 ov MDA fe kClN {30}
Dov F DN lDF Dd .Pw Pw FD ykh 1 rWF kl
: lOw pq oCp F D
ov C . D PvC C kl DNDA kClN
,111 ,107 ,105 ,103 ,101 ,97 ,93 ,87 ,81 ,63 ,57 ,45 ,43 ,33 ,13 ,9 ,1
,11 ,29 ,37 ,89 ,73 ,43 ,127 ,7 HNpN F D
ov C ok MDA kClN .113
V DF Co Dov C DoC pC .lOw 5 ,5 ,7 ,5 ,3 ,11 ,5 ,11 ,19 ,29
.129 kߡ MDA DoC W Ddok ,lA PvlF 137 kl ,l
.19*14= 266=129+137 : kߡ DoC V ФDd
lz TDF C
,lkp DC 9 ov F ok A k Dl peN {31}
PvC o 3
kl 129 kl DWA qC .kz A 129 CoCk 9 ov DN
FD 3pF DA MDA oDz pk Dov F xJ ,PvC Pw FD 3pF
Dov oDz C W . VN ,lOw o 3 lOw Pw
: kߡ V ФDd .765 kߡ MDA oDz W 71 kߡ
.19*44 D 71 + 765 = 836
lOvCi Dl peN o߮D ,kF A 129 CoCk 9 ov pC {32}
VN lOw pOF D A 129 CoCk Dov F lDF xJ , oDF D
W ,kF A 129 CoCk 9 ov pC . ClJ aC ov 8 .
.Pw Pw FD 19 pF ,1577
+129=1706 : l MDA kClN
F lDF Dd .[2] [1] ,loCk pO o k 129 128 ,127 kClC {33}
oDz V
DF . VN koCk 2 1 DNDA kClN Dov
ov pC .oA
PvlF Co 19*61 D 1159 kl ,MDA kClN DDF Dov
.Pw Pw FD 19 pF 1159+2=1161 l W ,kF A 129 CoCk 9
2 1 kl CoCk A MDA kClN o PvC Cov 9 ov {34}
5
ov : PvC NDi Z CoCk Pw pk ov þ .lzDG
: kߡ ov k C MDA kClN .PvC A 120 CoCk ,PvC o

: l W ,kF A 129 CoCk 9 ov pC .120+127=247=19*13
.Pw Pw FD
19 pF 247+2=249
.kp vopF Co koCk [2] [1] DA MDA kClN Co Dov {35}
D lߡ pz [1] DF DA MDA kClN Dov F lDF Dd
,16 ,12 ,11 ,10 ,9 ,6 ,5 ,4 : loCk NDi Z lOw ov 30 .
,91 ,87 ,86 ,82 ,66 ,65 ,64 ,63 ,62 ,61 ,60 ,49 ,37 ,23 ,21 ,20 ,18 ,17
,123 ,109 ,127 ,165 ,120 ,176 HNpN F DA MDA kClN .101 ,100 ,96 ,93
,19 ,12 ,12 ,18 ,11 ,11 ,14 ,13 ,18 ,182 ,118 ,112 ,135 ,110 ,111 ,128 ,111
: kߡ ov 30 C MDA oDz W .lOw 11 ,11 ,19 ,11 ,15 ,19 ,17
W ,kF A 129 CoCk 9 ov pC .19*6638
D 126122 (1+2+3+...+)
.Pw Pw FD 19 pF l 129+128+126122=126379 : MDA oDz
F Dd .19
DF kߡ Dw 9+1+2+7 PvC A 127 CoCk 9 ov {36}
D ,lߡ 19 DF Dw DA MDA ov DoC W D
ov
Dov oDz W PvC NDi Z CoCk ov 10 .
.19*64
D PvC 1216 DA MDA kClN
ov 3
.19 kߡ (1+2+7) DDF (9) ,PvC A 127 CoCk 9 ov {37}
DoC W
,9 kߡ DA ov DoC W Pw Ap DN ok pk
CoCk HNpOF DA .lOw 72 ,54 ,45 ,9 Dov C .10 kߡ DA MDA
kߡ ov v C
ok MDA kClN W .lOw A 28 ,55 ,37 ,127
.19*13 D 247
,lkp DkC Dl peN
o߮D ,kF A 129 CoCk 9 ov pC {38}
ov DoC W PzCk kV Ap ok pk ov þ PA
129 DF HpN C .27 ov DvC ,12 l NDA DoC W 9 l A
.koCl PFD Ap Do
l DF ,9 ov ok A
kl DWA qC .PvC A 129 CoCk 9 ov p lDF Dd {39}
Oh [9] F DA MDA kClN Dov F lDF ,kߡ Oh [9] F 129
[9] F
DA MDA kClN ClJ Ap ok ov 13 . D ,lߡ
,81 ,57 ,52 ,48 ,44 ,43 ,29 ,15 ,10 :
qC lNoDG Dov C .lߡ Oh
,49 ,29 ,59 ,89 ,69 ,99 ,109 HNpN F DA MDA kClN .104 ,96 ,87 ,82
Ap l DF koA Ch PvlF oDwF XDO .PvC 9 ,19 ,19 ,19 ,29 ,29
129 ,9 ov .oD EDwd F Co 9 ov Noߤ ok þ l PFD
19*33 D kߡ 627 ov 13 C MDA kClN W 9 ov lF .koCl A
: kߡ MDA oDz W DDF ,MDA kClN DDF ov oDz ,ԷF
F
qC DllJ C lzDF A 129 CoCk 9 ov pC .19*1245 D 23655
.Po lCh
Dd .kߡ Oh [9] o F NDA kClN kp PvC Cov 9 ov {40}
VN lߡ Oh [9] F DNDA kClN
kp Dov F lDF
19*34
D 646 Dov C ok MDA kClN Dov oDz W .
:
l W kF p C rV kF A 129 CoCk 9 ov pC .PvC
.Pw Pw FD 19 pF 646+129+9=784
lDF Dd .PvC A 127 CoCk 9 ov lz w PFDR Dd DN {41}
C ov 7 .
VN lߡ Oh [7] kl F DA MDA Dov F
.107 ,86 ,45 ,26 ,25 ,9 ,1 :
qC lNoDG Dov C ;loCk kV Z
W .7 ,17 ,37 ,227 ,77 ,127 ,7 qC lNoDG HNpN F DA MDA kClN
.19*42 D kߡ 798 ov P C MDA kClN DDF Dov oDz
koA
EDweF DF ,kz Oh [7] o F NDA kClN ov p ,CpFDF
.koCk PFD Ap l DF ,9 ov
A k Dl peN Z .PvC 127 126 ,9
ov phA A k {42}
DN VN Ap ov p phA A k F xJ ,lCkp DC pk
p phA A k F
ok [7] o kClN .oDء phA A k ok Co [7] Do
,127 DWF kF 129 ,9 ov A phA pC .19*2
D PvC 38 Ap ok ov
.Pp F
qC llJ C ,38 ,kF 37 [7] o oCpN kClN
Dov F VN lDF ,lzDF A
129 CoCk 9 ov Dp {43}
D A 129 CoCk Dov F D Dܷ lF ,loCk 129 A
,CpFDF .PvC A 286 Dz 2 ov DS CpF . D lOw pOF
Ap ok NDA DN DF Co A C D xKv .lzDG [129] oDz A
CoCk
A lOw ov 9 . V ,PvC lz N DA CpF 129 oDz
19
pF ov 9 C Dov oDz W PvC VN FD . loCk 129
PvC 19 F Pw FD A 129 W Ddok ,(114) PvC Pw FD
PvC lz O D F ,CpFDF . nd Co DA qC A 2 pF
, V 1161 DF Co 114 D .PvC DC A k CoCk ov 9 C qC
DF (1273) Co W C .19*67 D 1273 kߡ nd A qC kl 2
.l wD PvC lA
lF Pw ,44 ok W
Dov F lDF ,ok A k C DV kp i CpF {44}
9 ov Ckp p Dd
ok , D lOw 128 A CoCk
l DC D Pvp F Co 16 ov a .PvC A 129 CoCk
þ ,kߡ Pw FD 19 pF MDA Dov W .koCk A 128 Dk
,9 ov kp UoDh qC lF lzDF OzCk VN . nd Co 9 ov pC
nd qC
lF PvC V ФDd D 19*67 D kߡ 1273 W
9 ov l PFDR 첵 llJ C .koA PvlF 43 Pw ok A k
.lzDF OzCk 128 A lCO
127 126 A phA A k Ap CoDJ lF PvC Cov 9 ov {45}
phA A k oDz VN Ap CoDJ lF ov 85 F lDF .PvC
.lOw 7 6 ov phA A
k DS CpF . V DF Co ov p
175 A phA A k ;PvC 4 ov lF CoDJ lF ov .13
kߡ 6+7
CpF Co ص C .lA PvlF 351 A k C kp V DF .lOw 176
A k phA kߡ l~DN ,CpFDF .l DWC CoDJ lF Dov
.lOw 127 126
,9 ov
oCkCoDJ ,pF p ok Co Ap Dov phA A
k lDF Dd {46}
PvC fC . V DF Co ov p phA A k DoC ,CoDJ lF
Do l C vCF ,lz N C p
qC Ap ovp phA A k
,PvC 127 126 ,9 ov A k phA WO
ok .PvC lz PDd laJ
.129 128
F lDF .PvC o v CoCk
127 kl PvC A 127 CoCk 9 ov {47}
lNoDG Dov C ; VN PvC o v DA MDA kClN Dov
kClN .37 ,26 ,23 ,21 ,20
,18 ,17 ,16 ,12 ,11 ,10 ,9 ,7 ,6 ,5 ,4 ,3 ,2 : qC
,123 ,109 ,127 ,206 ,165 ,120 ,176 ,200 ,286 : qC lNoDG HNpN F DNDA
o phA Op p
ok DF .182 ,227 ,118 ,112 ,135 ,110 ,111 ,128 ,111
: kߡ D ФDd , DF DoC C V ,MDA kClN qC
CoCk 9 ov pC .19*4=76=2+7+8+2+5+0+1+8+1+3+9+7+6+5+0+6+0+6
DoC W ,7 DWF 9 l NDA kClN ok o phA ,kF A 129
.Pp F
qC llJ C 78 l
kp MDA Dd lDF ,PvC kp kl 9 ov ok MDA kClN DWA qC {48}
v DA MDA kClN koCk kV ov 8 .pF p ok 47 Pw ok Co
DA MDA kClN .26 ,20 ,17 ,12 ,11 ,10 ,9 ,6 Dov : PvC kp o
MDA C ok o phA .227 ,135 ,111 ,111 ,123 ,109 ,127 ,165 : kߡ
.19*2 D 38 kߡ DoC C W PvC 7 ,5 ,1 ,1 ,3 ,9 ,7 ,5 HNpOF
7 9 l A o phA ,kF A 129 CoCk 9 ov pC PvC fC
VN o߮D .Pw Pw FD 19 pF 40
l phA DoC W
.ߡ pNk k Oo Oo ,kߡ pOF MDA kClN o phA F D
. oD OzCk 48 47 Pw ok Dov qC Ovk D DF lDF {49}
Pvp qC Co Uq Dov lDF ,PvC kp ov 9 ov DWA qC
Co kp MDA DF ,kp Dov Dd . nd 47 Pw ok lz kCk D
.17 ,11 ,9 : Pw NDi Z DF ov v þ Ap DN ok .oCk
C ,kF A 129 CoCk 9 ov pC .PvC 111 ,123 ,127 DA MDA oDz
.Pp F
qC rC PG llJ
. oD lz oDzC DA F 49 Pw ok Cov v D DF lDF {50}
3 DA MDA
kClN (9 ov lD) lOw Ap kp Dov DC
.(9 ov lD) PvC kp DA MDA kClN ,(9 ov lD)
,PvC o
V DF N N Co DoC .lOw 111 123
,127 ov v C MDA kClN
C PvC lF .1+2+7+1+2+3+1+1+1=19 : kߡ D ФDd
.PvC A 127 CoCk 9 ov koCk OwF lz PFDR Pd C F llJ
CoCk Ap Dov DN CpF W ,kF A 129 CoCk 9 ov pC
,pk MoDG F .1+2+9+1+2+3+1+1+1=21 : l ,lkF NDi Z
.Pp F
qC Ap Do l rV C
,PvC kp DA MDA kClN (2) PvC kp DA kl (1) lOw ov v {51}
50 DN 48 Pw F) 9 ,11 ,17 Dov .PvC o 3 DA MDA kClN (3)
ФDd ,lƸV DF Co Dov C lk ǡN DoC þ .(lD Vo
.9+1+1+1+7=19 : kߡ
Dl peN o߮D 9 ov pC .PvC Pw FD 3 pF 129 kl {52}
kClN (2) kp kl DF (1) kF Cov PA ,PzCk A 129 ,l DkC
3 pF A MDA kClN (4) ,PvC kp A MDA kClN (3) ,PvC o 3 A MDA
Z CoCk koCk kV Ap DN ok ov 2 þ .PvC Pw FD
.A 111 DF 17 ov ,A 123 DF 11 ov :
lOw NDߥh
1+1+1+2+3+1+7+1+1+1=19 : kߡ MDA kClN ov oDz DoC W
.lzDF A 127 CoCk 9 ov kߡ lD Noߤ
ok þ C
MDA kClN (3) ,PvC kp A MDA kClN (2) ,PvC kp (1) 9 ov {53}
oDz (5) ,PvC C kl A MDA kClN (4) ,kߡ Oh [7] o F A
Z CoCk Cov k DN .PvC Pw FD 9 3 pF A ov
þ pC .PvC (A 37) 45 ov (A 127) 9 ov ,lOw NDi
: lz lCh Z WO ,l V DF Co DA DoC
9+1+2+7=19 4+5+3+7=19 ov k W =
19+19=38
ok ov k þ Moߤ C ok .PvC A 129 CoCk 9 ov p {54}
[9] F DA MDA oDz kߡ pz 9 DF DA oDz Pw Ap DN
oDz V ФDd .(A 19) 96 ov (A 129) 9 ov : kߡ Oh
19 pF 8828 kߡ ,MDA oDz W DDF ,MDA
kClN DDF ov
UoDh 9 ov qC Co (129 128) ok MDA Dd .Pw Pw FD
.19*451 D 8569 kߡ llV V . oCpN
Co MDGvDe
.PvC A 129 CoCk 9 ov p lDF {55}
Dov F lDF Dd .9+1+2+9=21 : kߡ DoC C W
. D 21
kߡ DA MDA kClN DDF DA ov oDz DoC W
.97 ,94
,68 ,37 ,27 ,25 ,9 ;lOw NDi Z CoCk ov 7
oDz W DDF ,ov
p ok MDA kClN F ov oDz kp DC DF
lDF Dd .Pw Pw FD 19 pF 34744 kߡ W ,MDA
W kߡ TDF C .127 , kDOvC 9 ov MDA fe kClN qC
.kz 19*1815
D ,34485
.PvC A 129 CoCk 9 ov p lDF oDF phA CpF {56}
FD 3 pF A oDz (2) ,PvC kp A oDz (1) oCk Cov DWC ok
oDz (4) ,PvC Pw FD 3 pF r 129 ,A MDA
kClN (3) ,PvC Pw
NDi Z CoCk pk ov
þ .kߡ Oh [9] o F MDA
FD 3 pF PvC 99 A MDA
k ClN ,PvC Pw FD 3 pF 15 ov : PvC
D ,kF A 129 CoCk 9 ov pC .kߡ Oh [9] o F ,PvC Pw
Co XDO C ,kp V DF Co ov k C Dov MDA oDz
: koA PvlF
129 ok kl D pC .Pw Pw FD 19 pF ,9 + 129 + 15 + 99 = 252
MDA kClN PvC kp A oDz oCk ov Ap ok ,qClDF ok Co
Dd .PvC 15 ov A ,kߡ Oh [9] o F ,PvC Pw FD 3 pF A
15 + 99 = 114 = 19 * 6 : oCk Co pq WO
ok pd Dh MD F z ok MDGvDe kClC qC ol {57}
CpD 9:127 ok MoDG phA .qCkpKF lC
lA 9:128-129 ok A k
ov ok pd phA CpFDF .(l DA) [ÿ] l fpN Co
phA PvC 129
phA A ,Dl peN DkC G .PvC [] pd 9
C F DF Dd .PvC [첵] ok phA Z PvC []
pd
kl oCl VN 9 ov DN Ap ClOFC qC ov p pd phA
lDF 9 ov d pd phA
ll D C . GvDe Co DA
.[] lzDF [] pd
pd phA ll Oh [] pd DF Co Ap Dov pC {58}
[] pd DF 9 ov lD ov 43 ߡ VO .oDءF ,PvC 9 ov
,30 ,29 ,28 ,27 ,26 ,23 ,21 ,16 ,15 ,12 ,11 ,10 ,9 ,7 ,3 ,2 ,1 : lߡ Oh
,68 ,67 ,66 ,63 ,62 ,61 ,58 ,51 ,49 ,46 ,44 ,43 ,40 ,39 ,38 ,37 ,36 ,32
kClN DDF Co Dov oDz þ pC .109 ,107 ,95 ,84 ,83 ,81 ,77 ,70
,CpFDF .1919 : kߡ ECV , ,lߡ Oh [] pd F Dov
[.] PvC [] 9 ov pd phA kߡ lDN CklW
VN (Pw C qC p Clh) [ C C ] V F lDF Dd {59}
19ok oDwF MoDG C .PvC lA 9:129 ok A ok MoDG C .
19 C D
ov oDz kp V DF .PvC lz oCpN GNp 29 Ap ov
,PvC lz oCpN DA ok [ C C ] MoDG NDA oDz DDF ,ov
C .19*112 D
,2128 kߡ V ФDd ,MoDG C oCpN kClN DDF
Ap F ϷO 9:128
' 129 koCk OwF PC C F rC PG WO
oDwF MoDG ,lD EDweF 9:129 pC PvC lF .Pw
.kp PFD Do l DF ,vC Ov C
[ C C ]
.73:9 ok oCpN phA ,PvC lA 2:163 ok [, C C ] oCpN C {60}
qC , MDA oDz W DDF ,MDA kClN DDF Co ov oDz pC
.19*16658 D
,316502 V ФDd ,oCpN phA DN ,oCpN C
F
qC llJ C ,kF DA Dz 9:129 ok A [ C C ] pC DOG
.Pp
DC C wF ,9 ov kDOC DV C wF F [ C C ] MoDG {61}
,20:98 ,20:8 ,13:30 ,11:14 ,9:31 ok ,PvC lz oCpN GNp 7 ,27 ov
.19*17 D ,323 kߡ D ФDd ,A 7 C kp V DF .27:26 ,23:116
.lz Op p
ok Ap kp DJ CpF Clh DS vo
p qC ,C Ϯ okD lw G DA kCk D CpF phDF {62}
A 127 CoCk 9 ov l PFDR kF oCp iz] PvC lz l Do
DMDGRC A qC Pw Cok .[PvC Clh DS vo ,h kDzo ,PvC
.PvC lz EDiOC ,Pw C DF A DGNoC pDiF lz kCk D oDءF
,PvC lz Oz (40:29 ,38) Ap ok o߮F [kDzo] kl oCl
o߮F [h] kl oCl .PvC 505 (4=k ,1=C ,300=y ,200=o)
(5=
@ 80= ,10= ,30= ,600= g ) ,PvC lz Oz (38:26) Ap ok
A DGlF [h] oCl A DGlF [kDzo] oCl Oz DF .PvC 725
kl ,ov C ok MDA fe kClN A DGlF 9 ov oDz
kߡ Dw PvC Pw FD 19 pF kl C .lD PvlF 5057259127
.19*266171533 DF
DN ,PvC lz ˡJ Clh DS vo DV ,3:81 qC MDA kClN {63}
.PvC (19*52) ,988 ,9 ov DDJ ,9:127
.PvC Pw FD 19 pF 9:127 DN 3:81 qC MDA oDz W {64}
[Clh] ,Clh DS vo ԵC qC G A 3 Pvok ,3:78 A ok {65}
F kqDw DA Co D (3:78) A C .lz kpF oDF (19*19) 361 kl
l DkC xKv ,kp lCh DC Ap F ok] CqDv ok qC
[.ll ok PGw Clh F OwCk DA ;PvC Ap
qC Ow
A DN ,kqDw oDzA Co Dl peN 3:78 A qC [Clh] {66}
.PvC lz oCpN (19*48) GNp 912 ,9:127
ok MDA ok ,3:78 ok MD kClN DDF ,pd kClN {67}
27
CoCk 3:78 A .143 ,ll Co W k p ,9:128-129
.PvC 28 pd 115 CoCk 9:128-129 ,pd
116 ,PvC
? P CO Z
OhDz Pvo F PDd PV Ϯ okD 첵 lCz
lCO peN a : koCn DF z b kp N DJ
p qC Ap pܵ p ,loCl ϷN Ap F 9:128-129 MDA ,lFD Co Ap F
ok oDwF oDwF DwC DCN qC lz OhCkpJ OhDv p F Do
N MDA Dov CpF DoDz ,MDA kClN ,Dov kClN-PvC
Ok ,pd kClN ,MD kClN , MCoDG oCpN kClN ,PvC lz
okD Clh vCF .ߥiF MD ط p D pF
.PvC lz dCp Ϯ

.kp Ch PDe A qC D ,Dw , ,CkDOvp Co pnN C D Dw
(15:9)

C lD Ap DN lz leO DF D
V DDwC pC] ,F
pl
F olZp Od ,loDF Co C lD lCO rp ,loDF
(17:88) [.l

a ,lA Dzkr D lCkp HnN Co Ap MDGRC Dw
ok ,kz A hCk lCO ok b .lC
kp HnN Co rr EDO
(41:41-42) .DOv FD ,d A qC rN ;lA ok Ozn

31 Ckld ,h pOk vN Clh PvCiF Ap Do rW D)
.lkp Dk DDw oDiOC Dezh TDF ClOFC ,lz oDzA ,J Dv
Ap qC lDF þ kp PFDR ,Ap ok Clh Do rW Z xKv
.lkp oDOhC Mv Ov DDw Oo Oo ,kz pJ
C HnN pF k OwCO Dk ok xa q phC Dv 32 C ok
ص C PvC O Clh o߮D Cpq .lk D C rCPz rW
DN lkCk pNKD F Co kh DFDO pk DkC Od . p PvC
pk k .lz VC Pwz DF DvDO DC !loA PvlF rZ lDz
Z] ,lCO kF C ,lkp HnN Co h pOk Ov DDw
þ DA qC pC DC [?!oCl G Co C D xJ ,Pw Dϵ qC h pOk
C] ,O Clh CpZ [?PvC FD 19 kl pF Ap O CpZ] ,lvpKF
DVpN F DS CpF .loCl FCV b [?koCk oCp 19 kl o pF Ap
1990 Dv qC G ok lz VpN voD DAp ok 15:87 74:30 A k C
(lD VN

Ap Do D rW Dlk qC lz DC A k -2

,C ,PvC lz ǡN Ap CoDJ oDZ qC PvC oCkCoDJ ov ,13 ov
pC Dd .PvC GNp 1482 ,13 ov ok DoDJ C oCpN klN W .o , ,
.PvC 11:11 ߡ VO , VN Ap A 1482 F
VN 11:11 DN Ap oCk CoDJ Dov MDA W F þ pC C
ov MDA oDz pC pk p qC .A 812 kߡ G ,
A 670 DA ߡ VO ,oDءF 9 ov phA DN Co CoDJ lF D
.lOw
PvC kl 812 670+812=1482 : kߡ , V 670 DF Co 812 pC
F lCO 1482 kl pk MoDG F .PvC Hp kl 670 ,Hp
.kz Pw ykh oCpN kClN Hp kl
DN oCkCoDJ Dov ok l oCn oDz [C wF] DF Co MDA pC
ov ,817=19*43 D ,A 817 kߡ A W , V DF 11:11
!C DeGv !PvC A 43 CoCk 13
.lzDF OzCk A 127 lDF 9 ov WOok

A DCoDJ kl oCl W .PvC 31 ov oCk CoDJ kp ov 9
1143 ,PvC 43 ov oCk CoDJ kp ov 11 .43*19 D 817 kߡ
.PvC 1362 Hp kl 1143 .9*127 : kߡ
!PvC 9:127 Ap ClOFC qC A 1362
A 27 ,PvC lA DA ok [Clh] PvC A 100 CoCk 9 ov
A 50 ok .Uq DN 50 PvC kp A DN 50 ,A 100 qC .PvC [Clh] lF
lF MDA 77+50=127 MDA W .loCk pFok Co [Clh] 77 ,kp
77;50=27 [Clh]
28 ,19 MDA lD 10kߡ A MDA DoC W Pw A 10 ,9 ov ok
Cl D .PvC 19 DA ok [Clh] oCpN klN W .p 37
NDA ok [Clh] 19 a !PvC 19 ov oCk CoDJ ov 10
!C DeGv .koCk kV ,PvC 9 DA DoC W

127 CoCk 9 ov ll MkDz lOw Clh wN D kClC
.l PGe [DN C kClC] oDF ok 9127 kl GNp C .PvC A
D CpF DCo CpZ CܷF CpA Clh koCk oCp 19 DJ o pF rZ
.ߡ okpv h bJ pJ laJ kClC ok DN PvC kp EDiOC
kl o߮Z G C .PvC C kl N8 PvC C kl 19
a DC ,PvC C kl 9127 kl .l ClJ DGNoC 9127 DF 819
.3049 ,3041 ,3037 .lzDG C pv PJ kl v W
.9127 =3049+3041+3037 ܷ
lOw kDq kClC .lOw DN C kClC a C kClC C
C kClC Z qC k 9127 kl .lzDF OzCk Co D PDh C
.PvC DN C kl v W lOw DN C kClC ܷ .lzDG
kClC aC lzDF OzCk VN .PvC 2287 C kl aC C
Co kl DoC pC C ܷ [ldC] o .PvC [ldC] DDoC o C
: DS CpF .1 D [ldC] kߡF ФDd kl phA , V ykh DF
9+1+2+7=19 ; 1+9=10 ; 1+0=1
2+2+8+7=19 ; 1+9=10 ; 1+0=1
ߡ VO ,oDءF lV C qC Co [DN C kClC] ,kClC lV ok pC
,272 HNpN F DA oCpN klN 3049 ,3041 ,3037 DN C kClC CpF
.PvC 274 ,273
272+273+274=819 .kߡ i DWC ok Clh D DC
!rZ Dh Clh dCp PvC Z

.PvC C kl 31 .PvC C kl 127 lzDF OzCk VN
kh DN oDءF 9 ov ok Co PvC lA DA ok [Clh] NDA pC
!PvC A 127 CoCk 9 ov l lDN 43 kߡ ,ov A 31 A
1131 PvC 31 C kl k11 .A 11 ,43 ,31 qC lF
lz oCpN oDF þ DA Pw [Clh] A 9127 kߡ ,C kl
.PvC
!PvC A 127 CoCk 9 ov kߡ l~DN oDFk ,9*127 kߡ 1143

phA DN Dov MDA W ,pF pok Co 9 ov MDA kClN pC
oDz , V DF Co PvC lz oCpN oDFk [C wF] DV 27 ov
: PzCk Ch Co pq D
93+227+77+64+118+78+112+135+
+98+110+111+128+99+52+43+111+123+109+127=2015

lzDF OzCk VN .Hp kl 1709 ,[Hp] PvC kl 2015 kl
P F kl C .PvC Ap DCoDJ kl oCl W 1709
FqC DF Ow Clh PvCiF p Dv l oDzC PV
.lz lCh phA Dk Po lCh
: l 20:15 A

p Cpq ,PzCk Ch D i DGpN CpA ,lA Dw PDv A]
[.lk xJ Co kh DصC CrV lDF w

.Pp FqC D rW C ,kF A 129 CoCk 9 ov pC l VN
A ok lCO pN a DN PvC kp oCn l Co Ap Clh aC
.kz ФDd

a .PvC [C wF] k CoCk 27 ov .PvC [C wF] lF 9 ov
qC 30 A ok kDOCDV [C wF] .koCk oCp ov 19 ,27 ov DN 9 ov qC
ov ok .PvC Hp kl 19 ,30 kl Cl .PvC lA 27 ov
A 19 ,30 A DN 12 A qC .48 12 MDA ok ,PvC lz oCpN oDFk 9 kl ,27
DF Co Dov MDA oDz pC a .48 DN 30 A qC o߮ ,PvC
27+12+27+30+27+48 = 171 = 9*19 : kߡ V
kߡ 927 kl .p pok Co 27 9 kl F Do FCo C
C kl N27 kClC lV ClOFC qC PvC C kl 103 kl .103*9
kߡ ,279 wF pC .27 ,9 F kp qDF oDFk WOok .PvC
9 F kpqDF oDFk WO ok ,127 kߡ C kl 31 .19*31
Cl a .PvC A 127 CoCk 9 ov l D F 127
.lz kDOvp Ap PvC ol Hz ,Hz N27 PvC 9 D Do

NDԬC DN .Ap D MCrW qC kF Ch lkp d Co aA
kV DFDO Dv~DO .PvC DFDO ok oCk kh loA kVF qC
.loCk oDwF MpD DF Dz DwC DpGOvk Dq op pDiF
ko CpF CDF pk ,Ap Do rW DF pG Clh Pdo F DC
.oCl Ap ok Do MDGRC
D Ap Do D MCrW DFok lz qD MCrW phA D CpF
.lpF "Dlz wN Dos" Pw Gz C rp F

PvC Clh F D wN ,OiGzh ro DN

U.S.I... P.O..Box. 251902.... Los Angeles, CA.. 90025