Least possible value for a modulo with given remainders

Hello guys. Im just asking how do you code a program that gets the LEAST value of a given modulo and remainder. Say example

Z = [3 4 5]
R = [2 1 4]

The inputs will give an output that gives the LEAST possible value for the given. So the answer to the above is 29.

[John D'Errico]

In general, you would use the chinese remainder theorem for problems of this ilk. Your question is not terribly clear though. Are you asking to solve for x, such that

mod(x,[3 4 5]) == [2 1 4]

You code it by writing the code. You COULD use intlinprog. if you think about the meaning of those modular equations.

mod(x,3) == 2

is equivalent to

x == 3*u1 + 2

likewise for the others. Then can you solve for x,u1,u2,u3, such that x is minimized, is non-negative, AND is integer, along with u1,u2,u3?

help intlinprog

[Riven Yvet]

Umm since i am given 3 modulos with remainders, there are a lot of possible values for that. How do i get the least possible though?

[Riven Yvet]

I can input any values of the modulo and remainder. the above is just an example input.