MathDB
Relating mean and gcd

Source: Kyiv City MO 2022 Round 1, Problem 8.1

January 23, 2022
number theoryalgebragreatest common divisor

Problem Statement

Consider 55 distinct positive integers. Can their mean be
a)Exactly 33 times larger than their largest common divisor?
b)Exactly 22 times larger than their largest common divisor?