Integer Sequences of the Form a^n + b^n
Number Theory
2010-04-26 v2
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.
Cite
@article{arxiv.1004.3799,
title = {Integer Sequences of the Form a^n + b^n},
author = {Abdulrahman Ali Abdulaziz},
journal= {arXiv preprint arXiv:1004.3799},
year = {2010}
}
Comments
11 pages, The 2nd International Conference on Mathematics & Statistics, 16-19 June 2008, Athens, Greece.