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## Main Question or Discussion Point

I have tried some values of a,b. And I guess the largest number not in the form of ax+by, (x,y are non-negative integers) with gcd(a,b)=1 is ab-a-b. But I don't know how to prove it. Can anyone give me some hints or directions? I don't want the detail proof,as I want to try it by myself. thank you

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