Let's say we have a real number, A, in the interval [0, 1). If we add another real number to it, it "Wraps" around back to zero.
So, for example:
Lets say: A = 5/13
If we multiply A by 2, we get: 10/13
If we multiple A by 3, we get: 2/13 (not 15/13)
If we multiple A by 4, we get 7/13 (not 20/13)
And so on...
My question is:
If given two such numbers, A and B, how can we find the smallest number, x, such that:
Ax = B
For example:
If A = 5/13 and B = 8/13, what do we need to multiply A by, to get B.
A solution for real numbers is preferable. However, if a solution does not exist for real numbers generally, then a solution for rational numbers should be sufficient.
Note that this problem is relevant to an algorithm that I'm writing. And I'd like to get it finished soon.
If I get my algorithm to work, and someone here provides a good solution, and that person (or people) have their name and contact details on their profile page, then I'm happy to give them a reference.