IMO 1984 LL SPA55

Let a, b, c be natural numbers such that a+b+c = 2pq(p30+q30),

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IMO 1984 LL SPA55

Origin: SPA

Problem

Let a, b, c be natural numbers such that a+b+c = 2pq(p30+q30), p > q being two given positive integers. (a) Prove that k = a3 + b3 + c3 is not a prime number. (b) Prove that if a \cdot b \cdot c is maximum, then 1984 divides k.