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X^2 + 1 = 0 (mod 5^3).

  1. Dec 20, 2004 #1
    How would i start to solve this problem?

    x^2 + 1 == 0 (mod 5^3).

    Find all solutions.

    How do i know how many solutions there are? If i reduce it to
    x^2 + 1 == 0 (mod 5), i get that x= 2,3,7,8,12, etc.
     
  2. jcsd
  3. Dec 20, 2004 #2
    ok, so now i know that it has 2 solutions, because x^2 + 1 == 0 (mod 5) has only two solutions, namely x= 4, x= -4.

    however f '(4) and f '(-4) are not congruent to 0 (mod 5). So these roots are nonsingular?
     
  4. Dec 20, 2004 #3

    Hurkyl

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