A^n + B^n = sum_(j = 0)^(⌊n/2⌋) (-1)^j n/(n - j)(n - j j)(A B)^j (A + B)^(n - 2j), where ⌊x⌋ is the floor function and (n k) is a binomial coefficient.

binomial number | binomial sums | Fermat's last theorem