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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
a2#b2$c2
.
%t perhaps could be sho&n (numerically) that !an#bn$cn
,o
r!
(a^n+b^n)/c^n=k =1
(Fermat's urface)(+eneralied Fermat's Last Theorem)
ho
lds true if and only if n$2*First try! -,
.,
/
(-2 # .2 $ /2)econd try! /,02,0-
(/2#022$0-2)Third
try: 6,
8,10
(12 # 2 $ 032)Fourth try! 0,
2,
sqr
t
(02 # 22 $ 2*2-12)44445First tryecond 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-*-/
0200200
2*33
200
00*.30*-00*-/0*-.
2100100100100
-3*6-3*.3*683*0.3*/.3*6/3*113*1/3*.03*13*/13*/813*-03*123*.3*/263*2.3*/63*.23*.13*03*/-3*-63*.083*0.3*.83*--3*-6033*003*./3*283*--003*383*.03*2/3*289n # yn $ 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$2
.
(ii) For other
triplet
s of number
s
it perhaps does not obey the same formula*(iii) ?ut generally speaing, from the @hart gi;en belo& it appears that!$>
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 (> 03 degree
s
c
ould be broen*(;)
W
e can mae
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 < 03 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)!
0G2G-G.G/G1G6Ghttp!==&&&*fortunecity*com=emachines=e00=1=mathe9/*htmlhttp!==&&&*economics*o9*ac*u=Jembers=giuseppe*maarino=FermatKJarchK233-*pdf http!==&&&*sidmore*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)

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