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2017 Polish Junior Math Olympiad Second Round P3

Source: 2017 Polish Junior Math Olympiad Second Round

May 22, 2023

number theory

Problem Statement

Let

a

b

, and

d

be positive integers. It is known that

a+b

is divisible by

d

and

a\cdot b

is divisible by

d^2

. Prove that both

a

and

b

are divisible by

d