Abstract
Let $G(m,k)=\max\lbrace \text{GCD}((n+1)^m+k,n^m+k)\ |\ n \in \mathbb N \rbrace$. The fact that $G(1,k)=1$ is trivial and Berzsenyi has shown that $G(2,k)=|4k+1|$. We give explicit formulas for $G(m,k)$ for $m=3,4,5$.
Citation
Les Reid. "On a Problem of Berzsenyi Regarding the GCD of Polynomial Expressions." Missouri J. Math. Sci. 17 (1) 3 - 11, Winter 2005. https://doi.org/10.35834/2005/1701003
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