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In this paper, we find all integer sequences of the form a^n + b^n, where aand b are complex numbers and n is a nonnegative integer. We prove that if pand q are integers, then there is a correspondence between the roots of thequadratic 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 forma^n - b^n. Finally, we use special values of a and b to obtain a range offormulas involving Lucas and Fibonacci numbers.

Integer Sequences of the Form a^n + b^n