# A Numerical Experiment on Fermat's Theorem (not intended as formal proof or disproof)

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Theorem: For any triplets of numbers (a,b,c) obeying Pythagorean theorem we have a^2+b^2=c^2.
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A Numerical Experiment on Fermat 's  Theorem  ( not intended as formal proof or disproof) V. Chrisitanto (vxianto@yahoo.com) F. Smarandache (fsmarandache@yahoo.com)  Fermat's "Last Theorem" asserts that if n > 2, the equation Theorem: For any triplet s of numbers (a,b,c) obeying ythagorean theorem we have a2#b2\$c2 . %t perhaps could be sho&n (numerically) that !an#bn\$cn ,o r! (a^n+b^n)/c^n=k =1 (Fermat's urface)(+eneralied Fermat's Last Theorem) ho lds true if and only if n\$2*First try! -,   .,   /   (-2 # .2 \$ /2)econd try! /,02,0-   (/2#022\$0-2)Third  try: 6,   8,10 (12 # 2 \$ 032)Fourth try! 0,   2,   sqr  t (02 # 22 \$ 2*2-12)44445First tryecond tryThird tryFourth try-,.,//,02,0-,0/,060,2,sqrt(/)7/7.03*017-1*/00*3/02*/72.*-.6*8-/*31*2/702*82-*1-*21-*-/ 0200200 2*33 200 00*.30*-00*-/0*-. 2100100100100 -3*6-3*.3*683*0.3*/.3*6/3*113*1/3*.03*13*/13*/813*-03*123*.3*/263*2.3*/63*.23*.13*03*/-3*-63*.083*0.3*.83*--3*-6033*003*./3*283*--003*383*.03*2/3*289n # yn \$ n cannot be sol;ed in integers 9, y, , &ith 9y <> 3 : http!==&&&*fortunecity*com=emachines=e00=1=mathe9/*html .  !onclu"ion s :   (i) %t is clear from the diagram that for the triplets  (-,.,/) and (/,02,0-) \$0 only at n\$2 . (ii) For other triplet s of number  s  it perhaps does not obey the same formula*(iii) ?ut generally speaing, from the @hart gi;en belo& it appears that!\$> For n # 2 \$\$% k ten&" % 1 ; \$> For n % 2 \$\$% k ten&" # 1 . (i;) For triplet s of numbers ( a,b,c ) , &hich do not follo& the ythagorean T riangle (> 03 degree s c ould be broen*(;) W e can mae an 'associate d  condition'! for the same triplet s of ( a,b,c )  follo&ing ythagorean theorem a"2#b"2\$c"2, it follo&s that for n\$3 then (a"n#b"n)=c"n\$ &ill yield \$2 (of course) .o r < 03 degree s ), i*e* w hen the triangle is on cur;ed7surface ,  then Fermat theorem 7/72*/32*//6*/0302*/3*330*332*33-*33.*33/*331*336*33*338*3303*3300*3302*330-*33 5umerical T est o n  Fermat 's  Theorem -,.,//,02,0-,0/,060,2,sqrt(/)  Eeferences (for similar simplified proof of Fermat 's   T heorem)!   0G2G-G.G/G1G6Ghttp!==&&&*fortunecity*com=emachines=e00=1=mathe9/*htmlhttp!==&&&*economics*o9*ac*u=Jembers=giuseppe*maarino=FermatKJarchK233-*pdf http!==&&&*sidmore*edu=academics=theater=productions=arcadia=math*htmlhttp!==&&&*fermatproof*com=http!==&&&*itsoc*org=re;ie&=3/pl0*pdf http!==yacas*sourceforge*net=Hlgochapter-*html  7] http://www.blackdouglas.com.au/webpapr/workmath/workmath.htm (Jan. 18, 2006)

Dec 16, 2018

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Dec 16, 2018
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