20100415, 01:20  #1 
"Bo Chen"
Oct 2005
Wuhan,China
2×5×17 Posts 
Ask a number theory question
This week I meet a problem that can't be solved by myself totally, so here it is.
Let a, b be two positive integers, a<b. Then what's the smallest number could be expressed as i*a+j*b, where i and j are integers, i>1,j>1. For example, if a=3,b=4,then c=6,since 5 can not be expressed as i*3+j*4 and 6=2*3+0*4,7=1*3+1*4,8=0*3+2*4,9=3*3+0*4,etc. And Then if a is an even number, b=a+1, it seems like c=a^2a, but I don't know how to proof it. Another question is if a is an odd number and b=a+2,how to compute c and is there a simple formula to express c? Thanks for your attention. Bo Chen 
20100415, 05:01  #2  
Aug 2005
Seattle, WA
3^{2}×199 Posts 
Quote:


20100415, 05:41  #3 
May 2003
7×13×17 Posts 
I think the problem is supposed to be: find the *largest* number which is *not* expressible in that form. This is often called the Chicken McNugget Theorem

20100415, 07:05  #4 
"Bo Chen"
Oct 2005
Wuhan,China
2·5·17 Posts 

20100415, 07:11  #5  
"Bo Chen"
Oct 2005
Wuhan,China
2×5×17 Posts 
Quote:
Thanks very much. 

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