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Old 2021-06-18, 02:11   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

953 Posts
Default Frobenius number

Today I learned,

about the 'coin problem'.
"With only a 2 pence and 5 pence coins, one cannot make 3 pence, but one can make any higher integral amount.

Very interesting

Similarly, with only an unlimited number of 2 pence ant 10 pence coins, you can only make positive even amounts of pence amounts. So there is no Frobenius number for the set (2,10) and GCD(2,10) = 2.

If (greatest common divisor) GCD(x,y) = 1 then there will be a Frobenius number , that is an amount for which any higher integral amount is possible.

For chicken McNuggets in quantities of 9 and 20, the Frobenius number is 151.

generally, this is my notation, Frobenius(a,b) = a*b - a - b.

Now I cite sources before I get something wrong.

Wikipedia Coin_problem

and another link from Art of Problem Solving Online

Chicken McNugget Theorem

enjoy

Matt

Last fiddled with by MattcAnderson on 2021-08-26 at 00:37 Reason: added Frobenius(a,b)
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