Miss Kate wants to test the mathematical skills of Jake and James. She sets up an integer x for them to guess and gives hints separately to both of them. Both of them are told that:
- x = a(mod b) and x=c(mod d)
- Both b and d are different primes larger than 20
- a and c are non-negative integers with a < b and c < d
- Only Jake is told the value of a and b, and only James is told the value of c and d.
She then sets up a meeting for them, but they aren't allowed to tell the others the values of a, b, c, or d. This is what they say:
- Jake: I don't know the number yet
- James: I don't know the number either
- Jake: Now I know the number
- James: I still don't know the number
What is the value of c?