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Proof of fermat's little theorem

  • 1. �o VI( J 1- () {(. Ar -l.u ~ ~r J 0 f , (h tH ;"j tkL P r-fl Of 111 CI <1fYX C ~-il)/7' L 0 f· fa fr-ov,ed : b' n-1f]- f , ove If*}" t> , . ,j 1.5 f vlllt' YJ qs n I J . .: {v 4 ~ + J
  • 2. h" - () + J) n _ ($ f J) h1 ~_( '2. 11-' (5 n -.s + n (, (d ) . ( 5) + fI (1. (J) (sJ .' ) No-f.: ce I R-f + CUl d- ~; J h +- VlJ (J.f- ($"-5) Qld (J . J)' fl,;s. Ij fyob(~f1'l (b~ - h) r: (J h (Ie / -ft "I.-+- f( ~ fCffl 5; 01), VII; ~ -ftre J(X. c Qft; Q r1 0.[ /X.f+ q"d ~iJ4lr (LI J -t./ZlV /h the '~ '0 "R' c! q b" /I e by (1 r ~ nvrn/;~~' Now ct.s (0" J os. If , f1,.e pR-V fIe -f1: I , .> -tJR fv fJ rf)..f r •
  • 3. Vljh ~ eric! tQk~ Gt- loo.k ( { r1 ;: ( ( :: 2 I 2. to{ 4 (l, = 5" i ..J (0 10 r J I S -,,' 21 ) 10 I 21 ,.. , q JI'oy V (,,( '" , Oil ~ {1,~ I.) I -;KCt -t- (S s~cl, -Ke,+ II ill' IJ Vv;~ ~ e)LC~ -(?<1~ 0+ b.J il~-t n· f.>ufI!"e
  • 4. .4- 11--.£ t I n - J , , ·-r-/....rc j 5 (i1 L1<;~<.v~e'l -.+'ha j'~ S CC:<"l dr',;J<c t LA ( , )(...- IA i~j.,d« .~ (;< Loo" n ::: .) 1o ) f 0 , s:: ,/ to / /0 ,/ > I" I I ) ... 7 LOb ~ q-l- ( - ~I ) 3 ,- ~J 21 5 5" ?/ 7 I/' bd L H., ..t · ;I , :s $ " -' . 5 ,- ,/ c!i.tl·,h -t1-Q / ,/ 1 ( cUI ··H 0" f tP r» ~ i, rll<' k'l," t S ..4. , {1,) .{ OI'kJ< Bv+ +0'. I? o » . r:' I"~ fll.{r'! ,b, ~ s n - - 4 -Fov ~-<q"""l'llt L.f 7 11 - 4 I 4 6 b er 6 V<./ -i ~()" ( c:; yltffl'il{" J((I" dt;; k {t..e 1 .., 1'l1 C C( ,., 1'0*
  • 5. n ]...0 J j 3b q I 1'1 • ,+ p. ) , ,.(. Sq",.e CiS #t~ c 0,1. r{ r c; ell { 5' Cl..f #.0 i-e . .b;DfI() ",iq I ( II( (l ( rn-r ~ 0'1 S 11, the I I L.; . ·fe 'f 1'0 J 0-1 .:1f.. G " "'c,,) Q'JM"( tll.{Y",{A"d -+1Y~~ It J' e
  • 6. r ur ' / ../- (/~~) s) .f '(, (I) (I)' ':t '(, (J ... (s"- s) Cittd v. : ((' r ~b~ - b) we ( CI1 t'hQ,/I (O/! t1'J1~"-! ~ in }1) SAc:, {( J<.'t" Qtl ~ Sf I;J- t/rl+;( w~ Orl< tfi:J 4 Cfi' ; 1h SulYl ~ .. (l II .. f1(2. (Il ~ (r) . f (11~r) (I - I) ..J. 11 ~ ( tl( J 11 ( Il( -It-.£. ; 911 Ix U' (1'. V v e rt bQ-f.()y K 1- -I J I - +e v'" s on R CI II J ,,:J ,'blc £j f' • IItC o o r» /7 s: y.> LAI.(; flCo'~ ( I ~ - I) ~.p -h h<1" J lit- How~vRv I" - ( (( ./ (~IH< I ..{u ZRVO r t't'~5f~cl ~ 'J Of wt.q-t II ., ·4f1J. 2~vv .. (s J.'vt ~; ble bJ 011) 11 (.(IY' "r- y .
  • 7. (j) H ~( ( sf 1/~ b 1'1 ._ k !A;1!: I f.A.;R; we hCh£ I he! J (f A _ f) J~.{ -f elf! d /, ,J ~~Irt~j 0 .... , . be;. wl-r.;ct.. J,' ,,'-J .. t (~ by 11 • -tv 2--C v o I ~£"(Q [ b" b] '5 JI' ,'j/bl£ ~ n CIS E· D· (q,.,..Q OJ. J-e, 5 hotA.IJ OJ. n;5 p Y00+ -f l'~iYlJ d +1, ill .1 /I''J elll I' s;-+! /'J Ot' /J1y bx-d fh 0 I • Pf (II J (,11 ) .fljl/l) (,I I m Jl, (""" J +"-,,. r: ..,' G'JQ;/l/ 411 1-l{ ~~Q d,) Co Ve'j O~- ~ 5f)~C; q I c h c; r~ c. .f-'f<:1 f'll-( fll b~f 5' r.(.-
  • 8. fll Y lr'.fA' 1 f,;{ -{Ce i-+ t ~-1-1 kr' ~lu(ef1 :I ('1 20 1J 1 A uJ+- R-r ee' ~~ ]"'" ] (J o '''3 hl1 N QJ (. T a l" ,.f d Q.f.Jev t~q J't c t.. q II c;" tJ- 1/(; Cl + --11-9:: • fl1.y /iflii' acJ;~('I<!hQ"~( I" aft -+ 1, '7~ Of> IJ (o C1 (OA d·t] , JQ'1/iA.J (v'' -I • e/] ' 1~r~ L a )tJ J'), I.( 4 ~ r: -I' e > (ft (5 },OtAU,) 011 I .f C{ L ~ Ci 4' 'f-+- J Sa i d I II r u.>~ fO/1yer 0 t1 I " , dO. No /'Yo ~,., j{ rill I"f'h" + (1 r. (I I' C .r c (' I ,A, .... .., Y'"1 ..