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I have a question

show that $x^4- y^4 = z^2$ has no nontrivial solution where $x$, $y$ and $z$ are nonzero integers

I tried infinite descent to find solution but I could not find it. square of a number in mod 4 is 1 or 0 I also tried to use but got nothing.

Can you help? thanks

  • 3
    This equation has infinitely many solutions, for example, $x=y=17$, $z=0$. You'll have a better chance of solving the problem if you get the statement right.2012-06-04
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    you are right. I edit it2012-06-04
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    @Brhn Please accept the answer if the answer is correct and you are satisfied with it, else please let us know if you have some more doubts.2012-08-04
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    See also: https://en.wikipedia.org/wiki/Fermat%27s_right_triangle_theorem2017-07-21
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    Related: https://math.stackexchange.com/questions/26548/how-to-get-fermats-descent-working-on-the-conic-x4y4-2z22018-11-25

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