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Discrete Math or modulus

  1. May 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the remainder of dividing 2(562009)-3.

    2. Relevant equations

    Let m be a positive integer. If a[tex]\equiv[/tex]b (mod m) and c[tex]\equiv[/tex]d (mod m), then a + c [tex]\equiv[/tex] b + d (mod m) and ac[tex]\equiv[/tex]bd (mod m).

    3. The attempt at a solution

    Using ac[tex]\equiv[/tex]bd (mod m):

    (2 mod 55)(562009mod 55) - (3 mod 55)

    Using a + c [tex]\equiv[/tex] b + d (mod m)

    (2 mod 55)((552009 mod 55) + (12009 mod 55)) - (3 mod 55)

    (2)(0+1)-(3) = -1 OR remainder of 54

    This was a problem on my math test and I got 52 as the remainder at first, but it was wrong.

    Thx if you can help me.
     
  2. jcsd
  3. May 18, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    54 is right, 52 is wrong. But your method is dubious. It looks like you are trying use a rule like (a+b)^n mod m=(a^n mod m)+(b^n mod m). That's not right. What is true is that a^n mod m=(a mod m)^n. Just use that 56 mod 55=1.
     
  4. May 18, 2009 #3
    Thanks so much =D, i'll remember that.
     
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