Prove that for all positive integers \(x,\)

\(\frac{x^5-1}{x-1}\) is never a perfect square.

This seems so simple but I don't see any efficient way of starting on this problem...

Thanks!!!

See the following:

Now, can you prove that \(x=3\) is the ONLY value of \(x\) for which \(\frac{x^5-1}{x-1}\) is a perfect square??

Tysm.

More info:

I tried different values of \(x\) up to \(10^8\)with a program and never was \(\frac{x^5-1}{x-1}\) a perfect square...

Can you find a proof?

thx

Alan proved what you asked and you did not even bother to thank him.

You did not even give him a point.

Why would any serious answerers bother with you?