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    Prove that if p is a prime number of the form 4n + 1

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    Prove that if p is a prime number of the form 4n + 1,
    then the following congruence holds:

    x^2 is congruent to -1 mod p.

    The more detail problem is in the attached file.

    © BrainMass Inc. brainmass.com April 4, 2020, 1:26 am ad1c9bdddf
    https://brainmass.com/math/number-theory/612643

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    The solution is in the attached file.

    Ring Theory 3
    Solving Congruences
    By :- Thokchom Sarojkumar Sinha

    Prove that if p is a prime number of the form 4n + 1
    then the following congruence holds,

    Proof :- Suppose that

    Since p = 4n + 1 then p - 1 = 4n
    which implies that

    Therefore the product for ...

    Solution Summary

    The solution explains the congruence: x^2 is congruent to -1 mod p.
    The solution is given in detail.
    This is mainly for solving the congruence by using the Wilson's theorem.

    $2.19

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