Two divisors of $(n^2+1)/2$ summing up to $δn + δ\pm 2$, $δ$ even

Sanda Bujačić Babić

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arXiv · 1707.00049

Two divisors of $(n^2+1)/2$ summing up to $δn + δ\pm 2$, $δ$ even

Sanda Bujačić Babić

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Abstract

We prove there exist infinitely many odd integers $n$ for which there exists a pair of positive divisors $d_1, d_2>1$ of $(n^2+1)/2$ such that $$d_1+d_2=δn+(δ+2).$$ We prove the similar result for $\varepsilon=δ-2$ and $δ\equiv4, 6\pmod{8}$ using different approaches and methods.

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BibTeX RIS

Sanda Bujačić Babić. 2017-06-30. Two divisors of $(n^2+1)/2$ summing up to $δn + δ\pm 2$, $δ$ even. https://arxiv.org/abs/1707.00049

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