View Single Post
Old 2010-04-15, 01:20   #1
wreck
 
wreck's Avatar
 
"Bo Chen"
Oct 2005
Wuhan,China

3×61 Posts
Default 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^2-a, 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--
wreck is offline   Reply With Quote