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59 in one way (Posted on 2011-08-13) Difficulty: 3 of 5
A and B are two positive integers such that:

1. The number 59 can be made by adding non-negative integral multiples of A and B in exactly one way.

2. Some numbers below 59 cannot be produced in this way at all, while some can be produced in one way and others in more than one way as sums of non-negative integral multiples of A and B.

3. All numbers above 59 can be produced in more than one way as sums of non-negative integral multiples of A and B.

What two numbers can A and B be?

See The Solution Submitted by Charlie    
Rating: 4.0000 (2 votes)

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Possible solution | Comment 4 of 7 |

Good problem.

A can be 4, and B can be 9, or vice versa. 59=27+32 (unique); all higher numbers can be made in at least 2 ways. A and B have to be relatively prime; they can't be too big or too small, and one has to be one more or less than a multiple of the other, to get all the numbers larger than 59 at least twice.

  Posted by broll on 2011-08-19 22:47:00
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