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Integer Sequences of the Form a^n + b^n by Abdulaziz, Abdulrahman Ali is a scholarly article available to read on EtoBox.

What is Integer Sequences of the Form a^n + b^n about?

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.

Author

Abdulaziz, Abdulrahman Ali

Published

2010

Language

EN