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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?

Note by Shourya Pandey
3 years, 7 months ago

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Its a nice theorem , and P14 in 104 number theory problems . For the proof , this link would help: AOPS-Chicken McNugget Theorem Shivang Jindal · 3 years, 7 months ago

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@Shivang Jindal Can you add this to the Brilliant Wiki of Chicken Mcnugget Theorem? Thanks! Calvin Lin Staff · 2 years ago

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@Calvin Lin Sure , i will add , with good description in 3-4 days. Shivang Jindal · 2 years ago

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