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GCD and LCM

Source: St Petersburg Olympiad 2011, Grade 9, P2

September 15, 2017
number theorygreatest common divisorleast common multiple

Problem Statement

a,ba,b are naturals and a×GCD(a,b)+b×LCM(a,b)<2.5aba \times GCD(a,b)+b \times LCM(a,b)<2.5 ab. Prove that b∣ab|a
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