Integer Sequences of the Form an + bn
Abstract
In this paper, we find all integer sequences of the form an + bn, 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 z2 - pz - q = 0 and integer sequences of the form an + bn. In addition, we will show that there are no integer sequences of the form an - bn. Finally, we use special values of a and b to obtain a range of formulas involving Lucas and Fibonacci numbers.
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