Re: A diofantine equation

On Sun, 10 Dec 2006, Mate wrote:
alainverghote@xxxxxxxx wrote:
Mate a écrit :

I seems that the equation 7^x + 2 = y^2
does not have integer solutions for x,y>1.
Can you suggest a method to prove this?

If x = 2k is even,
2 = (y - 7^k)(y + 7^k)
1 = y - 7^k
2 = y + 7^k
3 = 2y

Thus x is odd.

Is 'f' a greek letter ?

Je ne sais pas.
Anyway the name of the Greek mathematician is written in many
languages "Diofant" (vs. Diophant). It seems that this is accepted also
in english.
If it is more comfortable to you, please consider at the equation as a
diophantine one.

Please to honor the mathematician, Diophantine.
.

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