MHB Problem Chinese remainder Theorem

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The problem involves finding solutions for the equation \(x=x(r,s,t)\) where the intersection of the sets defined by \(r\), \(s\), and \(t\) is equal to \(x+n\mathbb{N}\). Participants clarify that \(n\) is the least common multiple of 2, 3, and 5, which is 30. The discussion focuses on determining the set of solutions that satisfy this condition. Understanding the role of the least common multiple is crucial for solving the problem. The conversation emphasizes the importance of clearly defining parameters in mathematical problems.
Julio1
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Find the set of solutions $x=x(r,s,t)$ such that $(r+2\mathbb{N})\cap (s+3\mathbb{N})\cap (t+5\mathbb{N})=x+n\mathbb{N}.$

Hello MHB :). Any hints for the problem?
 
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Hi Julio,

Could you specify what $n$ is? Is it $30$?
 
Euge said:
Hi Julio,

Could you specify what $n$ is? Is it $30$?

Hi Euge :).

Yes, $n=\text{lcm}(2,3,5)=30.$
 
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