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Romania EGMO TST 2022 Day 2 P4

Source:

February 15, 2022
number theoryromaniaEGMOprime numbers

Problem Statement

Let p≥3p\geq 3 be an odd positive integer. Show that pp is prime if and only if however we choose (p+1)/2(p+1)/2 pairwise distinct positive integers, we can find two of them, aa and bb, such that (a+b)/gcd⁡(a,b)≥p.(a+b)/\gcd(a,b)\geq p.
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