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Homework Help: Modular arith, number theory problem

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the number of roots for the equation [tex]x^2+1=0 \mod n \: for \: n = 8,9,10,45[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I have no idea where to start. Could someone help me understand?
     
  2. jcsd
  3. Sep 20, 2009 #2
    Do you understand what mod refers to?
     
  4. Sep 21, 2009 #3
    yea, mod is used to represent items in terms of base n. But I don't understand how that is going to change the number of roots in the problem
     
  5. Sep 21, 2009 #4

    lanedance

    User Avatar
    Homework Helper

    not sure but is this like modular arithmetic below?

    so for the case n = 2,
    try x = 0, 02+1= 1mod2 = 1 - FALSE
    try x = 1, 12+1= 2mod2 = 0 - TRUE
    x = 1 is the only for the n = 2 case

    so for the case n = 3,
    try x = 0, 02+1= 1mod2 = 1 - FALSE
    try x = 1, 12+1= 2mod3 = 2 - FALSE
    try x = 2, 32+1= 2mod3 = 0 - TRUE
    x = 1 is the only solution for the n = 3 case

    will start getting more intersting as the square get bigger and do more "loops" in the modular arithmetic...
     
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