Chicken McNuggets Theorem

It states that if gcd(m,n)=1 and m,n are natural numbers, then the largest number that cannot be written as the sum am+bn, where a,b are non-negative integers, is mn-m-n. Also, the number of mumbers that cannot be written in this form is (m-1)(n-1)/2. How does one prove this?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

Its a nice theorem , and P14 in 104 number theory problems . For the proof , this link would help: AOPS-Chicken McNugget Theorem

Shivang Jindal - 8 years, 3 months ago

Can you add this to the Brilliant Wiki of Chicken Mcnugget Theorem? Thanks!

Calvin Lin Staff - 6 years, 8 months ago

Sure , i will add , with good description in 3-4 days.

Shivang Jindal - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$