1. Prove that if b and c are odd, then (a/bc)=(a/b)(a/c)
2. Prove that if a==b (mod c), where c is odd, then (a/c)=(b/c)© BrainMass Inc. brainmass.com October 16, 2018, 4:50 pm ad1c9bdddf
For odd number P=p_1*p_2*...*p_s, where p_k are primes, the jacobi symbol (d/P) is defined as (d/P)=(d/p_1)(d/p_2)...(d/p_s), where (d/p_k) is the legendre symbol mod p_k.
1. If b and c are odd, ...
Jacobi Symbols and Proofs are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.
Discrete Math: Congruence Problem
Please provide a detailed solution to the following problem:
Let p be an odd prime and a such that (a, p) = 1. Show that the equation
x^2 = a (mod p^i)
has a solution for all i if it has a solution for i = 1. How many solutions are there?View Full Posting Details