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 March 5, 2021, 1:43 am ad1c9bdddf
The solution is in the attached file.
Ring Theory 3
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 ...
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.