Group Theory Questions. See attached file for full problem description.
( p is odd prime and a an integer not divisible by p ) the LEGENDRE SYMBOL IS DEFINRD BY = 1 if a is a quadratic residue of P, = -1 if a is a quadratic nonresidue of P.
b. Evaluate Hint 4567 is a prime.
c. Does 17 ( mod 29) have a solution ?
d. Does 19 ( mod 30) have a solution ?
e. Use Gauss's lemma to show that 17 (mod 19) is solvable.
f. Solve the congruence (mod 45).
g. Solve the congruence (mod 343).© BrainMass Inc. brainmass.com July 19, 2018, 7:48 am ad1c9bdddf
Please see the attached file.
For Legendre Symbol, we have the following properties which will be used in the following proof.
(2) (mod )
(7) Quadratic Reciprocity Theorem:
If both and are odd primes, then . In another word, if one of and is ...
This is a series of questions involving Gauss's lemma, congruences, and groups.