What are these type of problems called?

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In summary, the conversation discussed a math problem involving finding the smallest favorite number given certain remainders when divided by 5, 6, and 13. The purpose of this type of problem was questioned and it was identified as an arithmetic riddle or Diophantine problem. The problem was also related to the Chinese Remainder Theorem.
  • #1
shadowboy13
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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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  • #2
Arithmetic riddle?
 
  • #3
Diophantine problems involve finding solutions to a set of equations where the domain is restricted to the integers.
 
  • #4
Chinese Remainder Theorem problems?
 
  • #5
As johnqwertyful says, that's a classic CRT problem. The Wikipedia article also has a list of applications.
 

1. What are these type of problems called?

These types of problems are commonly referred to as scientific or research problems, as they require a systematic approach to finding a solution through experimentation and analysis.

2. Are there different categories of scientific problems?

Yes, there are various categories of scientific problems, such as theoretical problems, practical problems, and technical problems. Each category requires a different approach and methodology to solve.

3. How do scientists approach solving these types of problems?

Scientists use the scientific method to approach and solve problems. This involves identifying the problem, conducting research and gathering data, developing a hypothesis, designing and conducting experiments, analyzing the results, and drawing conclusions.

4. Can scientific problems be solved without experiments?

It depends on the nature of the problem. Some problems can be solved through theoretical analysis and existing data, while others require experimentation to gather new data and test hypotheses.

5. Is there a specific process for defining scientific problems?

There is no one specific process for defining scientific problems, as it can vary depending on the field of study and the problem itself. However, it often involves identifying a gap in current knowledge, formulating a research question, and determining the scope and limitations of the problem.

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