Journal of Integer Sequences, Vol. 24 (2021), Article 24.7.7

Representation of Integers of the Form x2 + my2z2

Supawadee Prugsapitak and Nattaporn Thongngam
Algebra and Applications Research Unit
Division of Computational Science
Faculty of Science
Prince of Songkla University
Hatyai, Songkhla 90110


Let m be a positive integer. A positive integer k is called m-special if every integer n can be expressed as n = x2 + my2kz2 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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