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Romania TST 2021 Day 1 P2

Source:

May 15, 2021
number theoryRomanian TSTTSTBritishMathematicalOlympiad

Problem Statement

For any positive integer n>1n>1, let p(n)p(n) be the greatest prime factor of nn. Find all the triplets of distinct positive integers (x,y,z)(x,y,z) which satisfy the following properties: x,yx,y and zz form an arithmetic progression, and p(xyz)≤3.p(xyz)\leq 3.
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