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Original scientific paper

A note on the products $((m+1)^{2}+1)((m+2)^{2}+1)\hdots(n^{2}+1)$ and $((m+1)^{3}+1)((m+2)^{3}+1)\hdots(n^{3}+1)$

Erhan Gürel ; Middle East Technical University, Northern Cyprus Campus,Güzelyurt, Turkey


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Abstract

We prove that for any positive integer $m$ there exists a positive real number $N_m$ such that whenever the integer $n\geq N_m$ neither the product $P^{n}_{m}=((m+1)^{2}+1)((m+2)^{2}+1)\hdots(n^{2}+1)$ nor the product $Q^{n}_{m}=((m+1)^{3}+1)((m+2)^{3}+1)\hdots(n^{3}+1)$ is a square.

Keywords

Polynomial products; diophantine equations

Hrčak ID:

157711

URI

https://hrcak.srce.hr/157711

Publication date:

16.5.2016.

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