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Homework Help: Determine if the congruence has solutions

  1. Nov 6, 2007 #1
    1. The problem statement, all variables and given/known data

    Determine if the congruence has solutions. If it does, determine the complete solution

    x^11 + 3x^10 + 5x ≡ 2 (mod 11)

    2. Relevant equations

    3. The attempt at a solution

    i know that 11 | x^11 + 3x^10 + 5x -2

    and where ax≡c (mod m) has a solutioon iff gcd(a,m) | c

    and thats about it

    i also know if x =1...then the gcd(11,9) | 2 ...meaning there is a solution

  2. jcsd
  3. Nov 6, 2007 #2
    The only thing I can think about is checking each number 1-10 to see which has a remainder of 2.
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