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Representation of Integers of the Form ***x*^{2} + *my*^{2} — *z*^{2}

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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*
= *x*^{2} + *my*^{2} − *kz*^{2}
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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