Chicken Mcnugget Theorem (Dartboard Problem)
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- Probably, I should begin by explaining what is perhaps the weirdest name for a math theorem in history. Although the problem had been explored by mathematicians like Frobenius a…
By Sagnik Majumder, William Chang, Andrew Wang
- Prove the generalization. Let a,ba, ba,b be natural numbers with gcd(a,b)=g\gcd(a, b) = ggcd(a,b)=g. Then every integer n≥(a−g)(b−g)gn\geq\dfrac{(a-g)(b-g)}gn≥g(a−g)(b−g) whic…
By amaterasu
- IMO 1983, Problem 3 Let a,ba, ba,b and ccc be positive integers, no two of which have a common divisor greater than 111. Show that 2abc−ab−bc−ca2abc-ab-bc-ca2abc−ab−bc−ca is the…
By amaterasu
- (USAMO 2001) Let SSS be a set of integers, such that (a) ∃a,b∈S\exists a,b \in S∃a,b∈S such that gcd(a,b)=gcd(a−2,b−2)=1\gcd(a,b) = gcd(a-2,b-2) = 1gcd(a,b)=gcd(a−2,b−2)=1. (b)…
By Sagnik Majumder, Moor Xu