Question regarding mod classes

  1. Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives
    a remainder of 4 in each case.

    I know I can approach this problem by writing the equivalence classes.

    x=4mod45 or x=4mod70

    I also know I can find x by multiplying 12*17*45 + 4, but this isn't the smallest positive integer.

    Can someone help me with a formula I can use?
  2. jcsd
  3. I like Serena

    I like Serena 6,181
    Homework Helper

    Erm... how about the solution x=4?
    It is a solution and I don't think there are any smaller positive integers that are also a solution.
  4. If you for some reason do not like the number 4, you have to add the lcm of your moduli to get the next.
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?