(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A given number [tex]x[/tex], if divided by 31, the remainder is 10, if divided by 73, the remainder is 35, if divided by 111, the remainder is 29. Then, what's the number [tex]x[/tex]?

2. Relevant equations

[tex]

x = 31k_1 + 10 = 73k_2 + 35 = 111k_3+29, \tex{ then?}

[/tex]

3. The attempt at a solution

I roughly remember this is a famous problem in high school mathematics, but I can't remember the way to solve this type of problems. The number of unknowns seem to be larger than the number of equations. I tried to write these equations in a way like,

[tex]

x = 111\times73\times31\times u_1

+73\times31\times u_2

+ 31\times k_3 + 10

[/tex]

But it seems to be not so helpful.

Any ideas? thanks in advance.

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# Homework Help: Number theory problem

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