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Omni-MATH / Alice thinks of four positive integers a≤b≤c≤d satisfying ab+cd,ac+bd,ad+bc=40,70,100. What are all the possible tuples (a,b,c,d) that Alice could be thinking of? · Discussion

Discussing Alice thinks of four positive integers a≤b≤c≤d satisfying {ab+cd,ac+bd,ad+bc}={40,70,100}. What are all the possible tuples (a,b,c,d) that Alice could be thinking of? · Omni-MATH

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