The largest divisor of 144 is 144 itself, but then $ m + n = 1 $, impossible. Next, try $ d = 72 $: then $ m + n = 2 $, so $ m = n = 1 $, which are coprime. Then $ a = 72 $, $ b = 72 $, and $ \gcd(72, 72) = 72 $. Valid. - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

$The largest divisor of 144 is 144 itself, but then $ m + n = 1 $, impossible. Next, try $ d = 72 $: then $ m + n = 2 $, so $ m = n = 1 $, which are coprime. Then $ a = 72 $, $ b = 72 $, and $ \gcd(72, 72) = 72 $. Valid.$

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