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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
