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Part of 2021 Polish Junior MO Second Round

Problems(1)

pos. integers a=b if (5a + 3b) is divisible by (a + b) (2021 Polish JMO R2 p3)

Source:

4/8/2021
Given are positive integers a,ba, b for which 5a+3b5a + 3b is divisible by a+ba + b. Prove that a=ba = b.
number theorydivisibledivides