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Math Help - quadratic congruence

  1. #1
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    quadratic congruence

    solve x^2=2 mod 100049

    i know that 2 is a QR since (2/p)=1

    i tried to consider x^2-2=0 mod p
    as well as looked at manipulating factors of p-1 and (p-1)/2

    the solutions are
    10948 and 89101

    please help me
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  2. #2
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    Quote Originally Posted by steiner View Post
    solve x^2=2 mod 100049

    i know that 2 is a QR since (2/p)=1

    i tried to consider x^2-2=0 mod p
    as well as looked at manipulating factors of p-1 and (p-1)/2

    the solutions are
    10948 and 89101

    please help me
    This is not a prime! It factors as 10049 = 13\cdot 773.

    It is therefore not solvable because (2/13) = (-1)^{(13^2-1)/8} = -1.
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  3. #3
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    the prime number 100049 is prime...
    three zeros.


    should i attempt trying to apply the CRT... and if so... HOW?

    i really thought I was onto something earlier with the factoring a quadratic...

    i have found similar algorithms on the internet solving quadratic congruences mod 53 and 19 and such, but i can not replicate them with successful results

    but i do know that 2 is a QR mod 100049 and is solvable...
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