Ah sorry, had a typo in the line that established 12^n-1 = 2^2n * 3^n - 1 .
Is showing 11 to be a factor, which happens to be prime, the same thing as showing that the prime factorization includes 11?
Homework Statement
Claim: If n is a positive integer, the prime factorization of 22n * 3n - 1 includes 11 as one of the prime factors.
Homework Equations
Factor Theorem: a polynomial f(x) has a factor (x-k) iff f(k)=0.The Attempt at a Solution
First, we show that (x-1) is a factor of (xn-1)...