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Representation of Integers of the Form ***x*^{2} + *k**y*^{2} – *l**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:**

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