1983 IMO Problems/Problem 3

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Let $a$, $b$ and $c$ be positive integers, no two of which have a common divisor greater than $1$. Show that $2abc − ab − bc − ca$ (Error compiling LaTeX. ! Package inputenc Error: Unicode char \u8:− not set up for use with LaTeX.) 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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