If a and b are two coprime numbers such that a + b = 41, then what is the maximum possible value of a × b?
420
With a+b=41 fixed, the product a×b is maximised when the two coprime numbers are as close to each other as possible.
Testing a=20, b=21 (consecutive integers, hence coprime): \(20\times21 = 420\).
Hence, the maximum possible value of a × b is 420.
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