+0  
 
+1
165
4
avatar+31 

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!!!

 Mar 12, 2022
 #1
avatar+33151 
+2

See the following:

 

 Mar 12, 2022
 #2
avatar+31 
-1

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.

ibhar  Mar 12, 2022
 #3
avatar+31 
-1

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

ibhar  Mar 13, 2022
 #4
avatar+117852 
+1

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?

 Mar 13, 2022

12 Online Users

avatar