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Number theory problem

  1. Dec 21, 2008 #1
    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
    x = 31k_1 + 10 = 73k_2 + 35 = 111k_3+29, \tex{ then?}

    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,
    x = 111\times73\times31\times u_1
    +73\times31\times u_2
    + 31\times k_3 + 10
    But it seems to be not so helpful.
    Any ideas? thanks in advance.
  2. jcsd
  3. Dec 21, 2008 #2


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    Staff Emeritus
    Science Advisor

    This uses the "Chinese remainder theorem".
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