Abstract
Let $f(x)=ax^{2^l\cdot3^m}+b\in \mathbb{Z}[x]$ be a polynomial with $l\geq 1, l+m\geq 2, ab\neq 0$ and such that $f(k)\neq 0$ for any $k\geq 1$. We prove, under $ABC$ conjecture, that the product $\prod_{k=1}^n f(k)$ is not a $2^l\cdot3^m$-th power for $n$ large enough.
Citation
Zhongfeng Zhang. "Powers in $\prod\limits_{k=1}^n (ak^{2^l\cdot3^m}+b)$." Funct. Approx. Comment. Math. 46 (1) 7 - 13, March 2012. https://doi.org/10.7169/facm/2012.46.1.1
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