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

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

2010-04-21

arxiv.org/abs/1004.3799v2

Essays on Mathematics and Statistics, Akis, V. (ed.), ATINER, 2009, pp. 85-95.

Mathematics

Number Theory

11 pages, The 2nd International Conference on Mathematics & Statistics, 16-19 June 2008, Athens, Greece.

Scientific paper

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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