IMO 1968 SL 21

Let a0, a1, . . . , ak (k \geq1) be positive integers. Find all positive

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IMO 1968 SL 21

Origin: CZS

Problem

Let a0, a1, . . . , ak (k \geq1) be positive integers. Find all positive integers y such that a0 | y; (a0 + a1) | (y + a1); . . . ; (a0 + an) | (y + an).

Solution

The given conditions are equivalent to y −a0 being divisible by a0, a0 + a1, a0 +a2, . . . , a0 +an, i.e., to y = k[a0, a0 +a1, . . . , a0 +an]+a0, k \inN0.