MathDB

1

Part of 2021 Czech-Austrian-Polish-Slovak Match

Problems(1)

Routine number theory

Source: 2021 Czech-Polish-Slovak Match, P1

8/3/2021
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)