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CAPS 2021 Problem 1

    Find all quadruples (a,b,c,d)(a, b, c, d) of positive integers satisfying gcd⁡(a,b,c,d)=1\gcd(a, b, c, d) = 1 and a∣b+c, b∣c+d, c∣d+a, d∣a+b.a | b + c, ~ b | c + d, ~ c | d + a, ~ d | a + b.

    Vítězslav Kala (Czech Republic)

    Dataset text AI-MO AoPS. Quoted with source.

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