Problem

Source: Iranian TST 2018, first exam day 2, problem 5

Tags: number theory proposed



Prove that for each positive integer $m$, one can find $m$ consecutive positive integers like $n$ such that the following phrase doesn't be a perfect power: $$\left(1^3+2018^3\right)\left(2^3+2018^3\right)\cdots \left(n^3+2018^3\right)$$ Proposed by Navid Safaei