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Basic Congruences Confusion

  1. Nov 12, 2012 #1
    Hi, this is not a homework problem, i just have a hard time following the sequence of this

    In the book , it shows a couple examples

    (=== is the triple equal sign)

    1) 26=19+7===3+7===10(mod8)
    2) 15=19-4===3-4=-1(mod8)
    3)38 = 19*2===3*2=6(mod8)
    4) 7===2(mod5), 343=7^3===2^3=8(mod5)

    I understand mod8 and whatnot, just how does the book go from 19+7 to 3+7, and from 19-4 to 3-4. I just don't get how 19 and 3 are logically connected

    I see how 15===-1(mod8) and 26===10(mod8) and 38=6(mod8).

    Any help understanding is appreciated
     
    Last edited: Nov 12, 2012
  2. jcsd
  3. Nov 12, 2012 #2
    The examples you cited are using the following property of congruences: If [itex]a \equiv b \pmod{m}[/itex], then [itex] a + c \equiv b + c \pmod{m}[/itex]. So, in your first example, let a = 19, b = 3, c = 7 and m = 8.

    Does that help?
     
  4. Nov 12, 2012 #3
    Any number A === A - N Mod N Thus 19 === 11 === 3 Mod 8, Therefore 19+7 === 3+7 and 19-4 === 3-4.
     
  5. Nov 12, 2012 #4
    Yes that makes a lot more sense now with a,b,c, and m after looking at the theorem.

    Thanks for you help
     
  6. Nov 12, 2012 #5
    thank you this also helped
     
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