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BALTIC-WAY 2021 Problem 17

  • Answer

Distinct positive integers a,b,c,da, b, c, d satisfy

{a∣b2+c2+d2,b∣a2+c2+d2,c∣a2+b2+d2,d∣a2+b2+c2,\left\{\begin{array}{l} a \mid b^{2}+c^{2}+d^{2}, \\ b \mid a^{2}+c^{2}+d^{2}, \\ c \mid a^{2}+b^{2}+d^{2}, \\ d \mid a^{2}+b^{2}+c^{2}, \end{array}\right.

and none of them is larger than the product of the three others. What is the largest possible number of primes among them?

Dataset text NuminaMath olympiads. Quoted with source.

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