Question

Let p be be prime and p ≡ 1 (mod 4|a|). Prove that a is a...

Let p be be prime and p ≡ 1 (mod 4|a|). Prove that a is a quadratic residue mod p.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let p be an odd prime. Prove that −1 is a quadratic residue modulo p if...
Let p be an odd prime. Prove that −1 is a quadratic residue modulo p if p ≡ 1 (mod 4), and −1 is a quadratic nonresidue modulo p if p ≡ 3 (mod 4).
Let p be a prime that is congruent to 3 mod 4. Prove that there is...
Let p be a prime that is congruent to 3 mod 4. Prove that there is no solution to the congruence x2≡−1 modp. (Hint: what would be the order of x?)
Let p be an odd prime, and let x = [(p−1)/2]!. Prove that x^2 ≡ (−1)^(p+1)/2...
Let p be an odd prime, and let x = [(p−1)/2]!. Prove that x^2 ≡ (−1)^(p+1)/2 (mod p). (You will need Wilson’s theorem, (p−1)! ≡−1 (mod p).) This gives another proof that if p ≡ 1 (mod 4), then x^2 ≡ −1 (mod p) has a solution.
Prove: If p is prime and p ≡ 7 (mod 8), then p | 2(p−1)/2 −...
Prove: If p is prime and p ≡ 7 (mod 8), then p | 2(p−1)/2 − 1. (Hint: Use the Legendre symbol (2/p) and Euler's criterion.)
Let gcd(m1,m2) = 1. Prove that a ≡ b (mod m1) and a ≡ b (mod...
Let gcd(m1,m2) = 1. Prove that a ≡ b (mod m1) and a ≡ b (mod m2) if and only if (meaning prove both ways) a ≡ b (mod m1m2). Hint: If a | bc and a is relatively prime to to b then a | c.
Let p be prime. Show that the equation x^2 is congruent to 1(mod p) has just...
Let p be prime. Show that the equation x^2 is congruent to 1(mod p) has just two solutions in Zp (the set of integers). We cannot use groups.
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0...
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0 (mod n), then a ≡ 0 (mod n) or b ≡ 0 (mod n). (b) Prove or disprove: Suppose p is a positive prime. If ab ≡ 0 (mod p), then a ≡ 0 (mod p) or b ≡ 0 (mod p).
prove that n> 1 and (n-1)!congruence -1(mod n) then n is prime
prove that n> 1 and (n-1)!congruence -1(mod n) then n is prime
Let p be a prime and let a be a primitive root modulo p. Show that...
Let p be a prime and let a be a primitive root modulo p. Show that if gcd (k, p-1) = 1, then b≡ak (mod p) is also a primitive root modulo p.
suppose that p is a prime with p= 3 ( mod 4). Show that for all...
suppose that p is a prime with p= 3 ( mod 4). Show that for all x in Z_p, it is not possible for both x and -x to be squares (x and -x cannot have a square root)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT