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arXiv · 1709.06337

Perfect numbers and Fibonacci primes (III)

Hao Zhong·Tianxin Cai
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Abstract

In this article, we consider the Diophantine equation $\sigma_{2}(n)-n^2=An+B$ with $A=P^2\pm2$. For some $B$, we show that except for finitely many computable solutions in the range $n\leq(|A|+|B|)^{3}$, all the solutions are expressible in terms of Lucas sequences. Meanwhile, we obtain some results relating to other linear recurrent sequences.

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Hao Zhong, Tianxin Cai. 2017-09-19. Perfect numbers and Fibonacci primes (III). https://arxiv.org/abs/1709.06337

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