What are these type of problems called?

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The problem discussed involves finding a number that meets specific remainder conditions when divided by 5, 6, and 13, with the solution being 154. This type of problem is related to the Chinese Remainder Theorem (CRT), which addresses systems of congruences. Participants in the discussion express curiosity about the classification and purpose of such problems, noting their connection to arithmetic riddles and Diophantine equations. The CRT is highlighted as a classic example of this mathematical concept, with references to its applications available on Wikipedia. Understanding these problems can enhance problem-solving skills in number theory.
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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.
 
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Arithmetic riddle?
 
Diophantine problems involve finding solutions to a set of equations where the domain is restricted to the integers.
 
Chinese Remainder Theorem problems?
 
As johnqwertyful says, that's a classic CRT problem. The Wikipedia article also has a list of applications.
 
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