  In this paper, we find all integer sequences of the form a^n + b^n, where a
and b are complex numbers and n is a nonnegative integer. We prove that if p
and q are integers, then there is a correspondence between the roots of the
quadratic equation z^2 - pz - q = 0 and integer sequences of the form a^n +
b^n. In addition, we will show that there are no integer sequences of the form
a^n - b^n. Finally, we use special values of a and b to obtain a range of
formulas involving Lucas and Fibonacci numbers.
