Questions askedfrom group or ring
kshashi9548 asked 3 months ago

1. Prove that if p is a prime number of the form 4n + 1, then there exists integers x, y and c such that
x2 + y2 = cp and gcd(c, p) = 1.
2. Prove that for a prime number p if there exists integers x, y and c such that x
2 + y2 = cp where c iscoprime to p then p can’t be a prime in Z[i].
5. Suppose that p is a prime in Z, but not prime in Z[i]. Then show that p = a2 + b2for some integers a and b


kshashi9548 replied 3 months ago

advanced problem