Problem Chinese remainder Theorem

[Julio1]

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?

 

[Euge]

Hi Julio,

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

 

[Julio1]

Hi Julio,

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

Hi Euge :).

Yes, $n=\text{lcm}(2,3,5)=30.$