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Modulus math problem help

  1. Nov 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Im confused as to how you obtain that,

    77 is congruent to -1 mod 26
    -77 is congruent to 1 mod 26
    -11 is congruent to 15 mod 26

    2. Relevant equations



    3. The attempt at a solution

    Some help would be great thanks
     
  2. jcsd
  3. Nov 4, 2009 #2

    lanedance

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    Re: modulus

    haven't worked a heap with mod, but i think the trick is that the remainder is positive, so for the first
    77 = 2x26 + 25, so 77mod26 = 25

    simlarly
    -1 = (-1)*26 + 25, then (-1)mod26 = 25
     
    Last edited: Nov 4, 2009
  4. Nov 4, 2009 #3

    Dick

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    Re: modulus

    a is congruent to b mod 26 if a-b is divisible by 26. 77-(-1)=78, -77-1=(-78), -11-15=(-26). All of the differences are evenly divisible by 26.
     
  5. Nov 4, 2009 #4

    lanedance

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    Re: modulus

    to clrify, i think mod is defined by the fact that if
    a mob n = b
    then (b-a) is a multiple of n

    so take a poitive number c, such that c<n, clearly
    c mod n = c
    now consider the negative case, say
    (-c) mod n = b
    then as c<n, and b>0, we must have
    (-c)-b = (-1)n
    so
    b = n -c
     
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