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?
+31 
