Representation of Integers of the Form x2 + my2 — z2
Supawadee Prugsapitak and Nattaporn Thongngam
Algebra and Applications Research Unit
Division of Computational Science
Faculty of Science
Prince of Songkla University
Hatyai, Songkhla 90110
Thailand
Abstract:
Let m be a positive integer. A positive integer k is called
m-special if every integer n can be expressed as n
= x2 + my2 − kz2
for some nonzero integers x, y and z. In this article, we
show that 1 is m-special if and only if m is not divisible
by 4.
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Received March 18 2021; revised version received April 6 2021;
July 10 2021.
Published in Journal of Integer Sequences,
July 19 2021.
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