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Cute NT with bounding

Source: Russian TST 2015, Day 10 P1 (Groups A & B)

April 21, 2023
number theoryprime numbers

Problem Statement

Prove that there exist two natural numbers a,ba,b such that ∣a−m∣+∣b−n∣>1000|a-m|+|b-n|>1000 for any relatively prime natural numbers m,nm,n.
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