Question 872663
r is idempotent ring where x^2 = x
Prove there exists some n such that
(x^n)^2 = x^n for all n>= 1
now for n = 1, we have 
x^2 = x which is true for x a member of r
for n+1 we need to show
(x^n+1)^2 = x^n+1
(x^n+1)^2 = (x^n * x)(x^n * x)
(x^n+1)^2 = (x^n)^2 * x^2
(x^n+1)^2 =  x^n * x
(x^n+1)^2 =  x^n+1