Representation of Integers of the Form x2 + ky2 – lz2
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:
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 + ky2 – lz2. 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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