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min, max pos. integer that divides exactly two elements of {1^2, .., 100^2}

Source: 2023 Peru MO (ONEM) L3 p1 - finals

May 11, 2024

number theorydividesPerfect Squares

Problem Statement

We define the set

M = \{1^2,2^2,3^2,..., 99^2, 100^2\}

. a) What is the smallest positive integer that divides exactly two elements of

M

? b) What is the largest positive integer that divides exactly two elements of

M