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Generalize (Posted on 2013-05-01) Difficulty: 3 of 5
Using only 4$ and 7$ bills, you could pay any integer number of dollars, greater than 17.
Prove it.

Given two coprime numbers a and b, what is the minimal number M(a,b) such that any amount greater or equal to M(a,b) can be expressed as p*a+q*b (p & q non-negative integers)?

How much is M(37,38)?

No Solution Yet Submitted by Ady TZIDON    
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Question Can you prove it? | Comment 4 of 5 |
This formula was also given in a comment to a problem years ago.  Would anyone care to give a nice proof that any amount greater than or equal to (a-1)(b-1)=ab-a-b+1 can be expressed?
  Posted by Jer on 2013-05-02 09:22:50
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