Question 1006373
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