- #1
adamg
- 48
- 0
this is quite a classic problem i think but I am having difficulty finishing it off. If we have two stamps of positive values a and b, (greater than 1), what values can be expressed as a linear combination of these 2 stamps. If the stamps have a highest common factor greater than 1, then there are infinitely many 'bad' numbers. But if the numbers are coprime, after a certain point, all numbers are possible. For instance, with 5 and 8, in the list of possible numbers, you eventually get 28,29,30,31,32, therefore by adding 5's every other number is possible.
Can anyone help me prove the fact the if you have a and b, with a<b, then eventually you get 'a' consecutive numbers in the list of possibles. (therefore making all subsequent numbers possible).
Any other angle welcome!
Can anyone help me prove the fact the if you have a and b, with a<b, then eventually you get 'a' consecutive numbers in the list of possibles. (therefore making all subsequent numbers possible).
Any other angle welcome!