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Iran number theory

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

April 8, 2018
number theory proposed

Problem Statement

Prove that for each positive integer mm, one can find mm consecutive positive integers like nn such that the following phrase doesn't be a perfect power: (13+20183)(23+20183)⋯(n3+20183)\left(1^3+2018^3\right)\left(2^3+2018^3\right)\cdots \left(n^3+2018^3\right)
Proposed by Navid Safaei
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