Powers in \(\prod_{k=1}^n (ak^{2^l\cdot3^m}+b)\) (Q2428761)

Let \(f(x)=ax^{2^l3^m}+b \in \mathbb{Z}[x]\) be a polynomial with \(l \geq 1, l+m \geq 2, ab \neq 0\) such that \(f(k) \neq 0\) for any \(k \geq 1\). In this paper it is proved that under the ABC conjecture the product \(\prod_{k=1}^n f(k)\) is not a \(2^l3^m\) power for \(n\) large enough.