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MathNet 2018-part-04 — 181 problems (EN–VI) Question 122

Math Olympiad Vault · MathNet 2018-part-04 — 181 problems (EN–VI)

Question 122

Find the distinct positive integers $a$, $b$, $c$, $d$, such that the following conditions hold:
(1) exactly three of the four numbers are prime numbers;
(2) $a^2 + b^2 + c^2 + d^2 = 2018$.