I did a problem for my teacher (literally speaking) that he was having trouble remembering, and it was relatively weird for a math problem. It said: "If i divided my favorite number by 5, i get a remainder of 4. If i divide by 6 i get a remainder of 4; lastly if i divide my favorite number by 13, i get a remainder of 11, what is my smallest favorite number? First of, it's 154, but what is the purpose of this type of problem? He said he had gotten it from youtube, but i don't even know where to look for it, to find it's purpose atleast. Can anyone help me? I'm kinda curious as to these type of problems.
Diophantine problems involve finding solutions to a set of equations where the domain is restricted to the integers.
As johnqwertyful says, that's a classic CRT problem. The Wikipedia article also has a list of applications.