Break a number into factors.

Question

I want to split a number in a product of factors, i am not sure how to do it.

(2^48)+1

I think it should involve either mersenne or fermat little theorem. I have factored 48 and i have [(2^2^4)*2^3]+1

Answer 1

Hint: Use the factorization $a^3+b^3 = (a+b)(a^2-ab+b^2)$ for certain values of $a$ and $b$.

FYI: According to Wolfram Alpha, $2^{48}+1$ is the product of $3$ primes, so it is hard (but not impossible) to do better than the factorization I suggested.