Does there exist an arithmetic progression with $2017$ terms such that each term is not a perfect power, but the product of all $2017$ terms is?
Problem
Source: 2018 Thailand TST 1.3
Tags: number theory, arithmetic sequence
Tung-CHL
23.04.2022 10:49
MathLover_ZJ wrote: Yes.
$2017!,2017!\cdot 2,\cdots,2017!\cdot 2017$
This is correct by the fact that $2017$ is a prime number. I wonder how does it work for composite number, for example $2016$?
MathLover_ZJ
23.04.2022 11:02
Tung-CHL wrote: MathLover_ZJ wrote: Yes.
$2017!,2017!\cdot 2,\cdots,2017!\cdot 2017$
This is correct by the fact that $2017$ is a prime number. I wonder how does it work for composite number, for example $2016$? It's right for all odd numbers.I don't know how to deal with even numbers.