24/7

What is the largest integer that cannot be expressed in the form 24 a + 7 b 24a + 7b where a a and b b are non-negative integers?


The answer is 137.

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4 solutions

This is a version of "The Coin Problem".

(For a discussion see here .)

Since 24 24 and 7 7 are relatively prime, the solution is

24 7 24 7 = 137 24*7 - 24 - 7 = \boxed{137} .

aka Chicken McNugget Theorem :) See link from AOPS

Happy Melodies - 6 years, 9 months ago

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overleveled i think

math man - 6 years, 9 months ago
Ahaan Rungta
Aug 23, 2014

By the Chicken McNugget Theorem , the answer is 24 7 24 7 = 137 . 24 \cdot 7 - 24 - 7 = \boxed {137}.

Rutvik Paikine
Aug 23, 2014

We have to find THE FOBRENIUS NUMBER.........Which is equivalent to.... {[a-d][b-d]/d}-d........where gcd(a,b) is d......and ax+ by....therefore.....137!

Arya Samanta
Aug 22, 2014

Well I'll tell you a thing..for every gcd ( x , y ) = 1 \gcd(x,y)=1

a x + b y = m a n y n u m b e r s . . . ax+by= \cdots many numbers... [ x , y Z + x,y \in \mathbb{Z^+} (I am not sure on this) ] also not to forget a , b n o n . n e g a t i v e Z a,b \in \mathbb{non.negative} \mathbb{Z}

the total no. of numbers which cannot be expressed in this form are

( x 1 ) ( y 1 ) 2 \frac{(x-1)(y-1)}{2} ...now here I can't have to prove it

and the highest of them..is ( x 1 ) ( y 1 ) 1 \boxed{(x-1)(y-1) - 1} ...

now get it..

It is known as the Fobrenius number

Rutvik Paikine - 6 years, 9 months ago

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