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

Abdulrahman Ali Abdulaziz

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arXiv · 1004.3799

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

Abdulrahman Ali Abdulaziz

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Abstract

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.

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Abdulrahman Ali Abdulaziz. 2010-04-23. Integer Sequences of the Form a^n + b^n. https://arxiv.org/abs/1004.3799

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