Re: Does x^2+y^2=z^50 have integer solutions?

Bill Dubuque wrote:


I wasn't purporting to give a complete answer to the question.
I was just pointing out that it reduces to the question of which
n are expressible in the form x^2 + y^2. I mentioned Hardy & Wright,
reference to which would answer the question completely.

Reference? I don't recall H&W treating sums of _nonzero_ squares.
I don't see how you expect the OP to have any hope of attaining
such a reduction - esp. not merely from what you wrote above.

Aren't you being a bit ridiculous?
It is obvious how to extend the argument in Hardy & Wright
to cover the strictly positive case.

To repeat my point: the original question
really reduces to determining when n can be expressed as x^2 + y^2.
The additional condition that x,y > 0 only makes the argument
slightly messier.

I wasn't purporting to give the OP a complete answer;
I was just pointing out the simplest way to get such an answer.

.

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