Solutions to the Diophantine Equation x2 + 16 ∙ 7b = y2r

Abstract

We present a method of determining integral solutions to the equation x2 + 16 ∙ 7b = y2r, where x, y, b, r ∈ ℤ+. We observe that the results can be classified into several categories. Under each category, a general formula is obtained using the geometric progression method. We then provide the bound for the number of non-negative integral solutions associated with each b. Lastly, the general formula for each of the categories is obtained and presented to determine the respective values of x and yr. We also highlight two special cases where different formulae are needed to represent their integral solutions. © Copyright Yow. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.