arXiv subjects

Abdulrahman Ali Abdulaziz

Publications and source records attributed to Abdulrahman Ali Abdulaziz.

2 recordsLinked to original sources

arXiv2010

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

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.

math.NT↗

arXiv2010

The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples

Ever since it was published by Neugebauer and Sachs in 1945, the Old Babylonian tablet known as Plimpton 322 has been the subject of numerous studies leading to different and often conflicting interpretations of it. Overall, the tablet is more or less viewed as a list of fifteen Pythagorean triplets, but scholars are divided on how and why the list was devised. In this paper, we present a survey of previous attempts to interpret Plimpton 322, and then offer some new insights that could help in sharpening the endless debate about this ancient tablet.

math.HO↗