SOLUTION: Hi ! Here is the problem : Find all the values of the integer x so that : {{{ x^4+x^3+x^2+x+1= n }}} Where n is a perfect square. I may have found somewhere to start, but I real

Question 1006373: Hi ! Here is the problem :
Find all the values of the integer x so that :

Where n is a perfect square. I may have found somewhere to start, but I really don't know where to search then :

I really need help !
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
This is a geometric series
1 + x + x^2 + x^3 +x^4
The partial sum of a geometric series is
a (1 - r^n) / (1 - r)
For this problem a = 1, r = x, and n = 5
(1 - x^5) / (1 - x)
We pick values of x that produce a perfect square
there is one solution - x = 3, n = 121

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