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1

Part of 2022 Saint Petersburg Mathematical Olympiad

Problems(1)

a+k divides b+k for all k<b implies a-k|b-k for all k<b

Source: St Petersburg 2022 9.1

9/28/2022
The positive integers aa and bb are such that a+ka+k is divisible by b+kb+k for all positive integers numbers k<bk<b. Prove that a−ka-k is divisible by b−kb-k for all positive integers k<bk<b.
number theory