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arithmetic progression of 2016 terms whose product is perfect power

Source: 2016 Argentina OMA Finals L3 p1

January 16, 2023

number theoryPerfect powerarithmetic sequence

Problem Statement

Find an arithmetic progression of

2016

natural numbers such that neither is a perfect power but its multiplication is a perfect power.
Clarification: A perfect power is a number of the form

n^k

where

n

and

k

are both natural numbers greater than or equal to

2

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