Chicken McNugget Theorem

The Chicken McNugget Theorem (or Postage Stamp Problem or Frobenius Coin Problem) states that for any two relatively prime positive integers $m,n$, the greatest integer that cannot be written in the form $am + bn$ for nonnegative integers $a, b$ is $mn-m-n$. 

A consequence of the theorem is that there are exactly $\dfrac{(m - 1)(n - 1)}{2}$ positive integers which cannot be expressed in the form $am + bn$. The proof is based on the fact that in each pair of the form $(k, mn-m-n-k)$, exactly one element is expressible.

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