Q1.a) Assume known that 857 and 503 are primes. Determine
whether 503 is a quadratic residue modulo 857 or not.
b) Slove the second-degree congruence equation 2x2+
3x-11congruent (mod 31)
c) calculate the remainder when 73333+
2516178 is divided by 11
(a). Prove the law of quadratic reciprocity for odd primes.
Include all definitions and results used throughout the proof.
(b). Explain why it is enough to prove the reciprocity law for 2
and the quadratic reciprocity law for odd primes to answer the
general question: Is m a square mod n for any positive integers m,
n?
(c). Describe the role of permutations in the proof of quadratic
reciprocity.