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Math Help - Find all solutions, if any

  1. #1
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    Find all solutions, if any

    Find all solutions, if any, to each of the following congruencies:

    (x^2) -2 is congruent to 0(mod7)

    (x^3)-2x+3 is congruent to 0(mod7)

    I dont know if I am doing this right this is what I did
    gcd(1,-2,7)=1
    so there are 1*7 possible solutions
    x= 0, 1, 2, 3, 4, 5, 6
    solutions of x
    -2 not congruent to 0(mod 7)
    -1 not congruent to 0(mod 7)
    7 congruent to 0(mod 7)
    14 congruent to 0(mod 7)
    23 not congruent to 0(mod 7)
    34 not congruent to 0(mod 7)

    so are the solutions 3 and 4 or am i doing it wrong.
    I found the second congruency has no solution I hope!!!
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    Find all solutions, if any, to each of the following congruencies:

    (x^2) -2 is congruent to 0(mod7)

    (x^3)-2x+3 is congruent to 0(mod7)
    Just check x=0,1,2,3,4,5,6.
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