Finite sequences of integers expressible as sums of two squares

Ajai Choudhry; Bibekananda Maji

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arXiv · 2310.13317

Finite sequences of integers expressible as sums of two squares

Ajai Choudhry·Bibekananda Maji

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Abstract

This paper is concerned with finite sequences of integers that may be written as sums of squares of two nonzero integers. We first find infinitely many integers $n$ such that $n, n+h$ and $n+k$ are all sums of two squares where $h$ and $k$ are two arbitrary integers, and as an immediate corollary obtain, in parametric terms, three consecutive integers that are sums of two squares. Similarly we obtain $n$ in parametric terms such that all the four integers $n, n+1, n+2, n+4$ are sums of two squares. We also find infinitely many integers $n$ such that all the five integers $n, n+1, n+2, n+4, n+5$ are sums of two squares, and finally, we find infinitely many arithmetic progressions, with common difference $4$, of five integers all of which are sums of two squares.

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BibTeX RIS

Ajai Choudhry, Bibekananda Maji. 2023-10-20. Finite sequences of integers expressible as sums of two squares. https://arxiv.org/abs/2310.13317

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