1983 IMO Problems/Problem 4

Problem

Let $a$ , $b$ and $c$ be positive integers, no two of which have a common divisor greater than $1$ . Show that $2abc - ab - bc - ca$ is the largest integer which cannot be expressed in the form $xbc + yca + zab$ , where $x$ , $y$ and $z$ are non-negative integers.

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1983 IMO Problems/Problem 4

Problem

Solution