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On the equation x2 + ry2 = z2

Published online by Cambridge University Press:  14 February 2019

Emrys Read
Emrys Read*
Affiliation:
5 Cefn Cynrig, Bethel, Caernarfon, Gwynedd LL55 1UW e-mail: mairacemrys@btinternet.com
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Extract

In this Article, we derive a method for classifying all positive integer solutions of the equation x2 + ry2 = z2, where r is a given positive rational. In order to simplify notation, such a solution with x = a, y = b and z = c will be denoted by the ordered triple (a, b, c) and, in all that follows, the term solution will be taken to mean a positive integer solution of the above equation. The method employed will be similar to that used in [1] to find all integer triangles containing an angle whose cosine is known.

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 556 , March 2019 , pp. 87 - 93
Copyright
Copyright © Mathematical Association 2019 

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References

1. Read, Emrys, On integer triangles, Math. Gaz., 98 (March 2014) pp. 107–112.10.1017/S0025557200000735Google Scholar
2. Jones, Gareth A. and Mary Jones, J., Elementary number theory, Springer (2002).Google Scholar