Journal of Integer Sequences, Vol. 25 (2022), Article 22.8.5

Representation of Integers of the Form x2 + ky2lz2

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


A positive integer l is k-special if for every integer n there exist non-zero integers x, y, and z such that n = x2 + ky2lz2. For all odd integers k, we find infinite classes of k-special numbers and 2k-special numbers.

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Received November 10 2021; revised versions received December 21 2021; April 15 2022; April 24 2022; October 18 2022; October 24 2022. Published in Journal of Integer Sequences, October 25 2022.

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