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Topic: Diophantine FLT similar system -No solution Proof!
Replies: 12   Last Post: Feb 7, 2014 9:24 PM

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 Jimmy Timmermans Posts: 6 Registered: 2/4/14
Diophantine FLT similar system -No solution Proof!
Posted: Feb 5, 2014 6:16 PM

Let x,z coprime in N*
a,b in Z*

(I) (1-yb)x^n+by^n = z^n,
(II) x-z=yba

It is slightly modified Fermat equation.

How to proof that this system doesn´t have solution?

I found solutions (n=3) for (I) a(x^n-z^n)/(x-z) = (-y^(n-1)+x^n)]
using mod a(x^n-z^n)/(x-z),

but this doesn´t satisfy x-z=yba.

I didn´t find a contradiction :

(-1)^n = b^(n-1) a^n (mod x)
x=z (mod y)
b^(n-1)a^n(1-yb)=-1 (mod z)

Jimmy

Date Subject Author
2/5/14 Jimmy Timmermans
2/5/14 quasi
2/6/14 Jimmy Timmermans
2/6/14 Peter Percival
2/6/14 Port563
2/6/14 Pubkeybreaker
2/6/14 Pubkeybreaker
2/6/14 Peter Percival
2/6/14 Port563
2/6/14 Brian Q. Hutchings
2/7/14 Brian Q. Hutchings
2/7/14 Brian Q. Hutchings
2/6/14 Jimmy Timmermans