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MathNet 2018-part-05 — 181 problems (EN–VI) Question 77

Math Olympiad Vault · MathNet 2018-part-05 — 181 problems (EN–VI)

Question 77

Distinct prime numbers $p$, $q$, $r$ satisfy the equation
$$
2 p q r + 50 p q = 7 p q r + 55 p r = 8 p q r + 12 q r = A
$$
for some positive integer $A$. Find $A$.