Determine the odd primes p for which −26 is a square mod p

Question

Question

Answer 1

Answer #1

for have such primes (Odd), we many primes which Qu - 26 = n² mod Р let for m-1 ule have -265 12 mod p -26-15 o mod p -27= o x

Answer 2

Similar Homework Help Questions

Suppose that pı, P2, ..., P, are the only primes congruent to 1 (mod 4). Prove...

Suppose that pı, P2, ..., P, are the only primes congruent to 1 (mod 4). Prove that 4p?p, ... p, + 1 is divisible only by primes congruent to 3 (mod 4). Assuming that all odd prime factors of integers of the form x2 +1 are congruent to 1 (mod 4), use Exercise 6 to prove that there exist infinitely many primes congruent to 1 (mod 4).
6. Let n be any positive integer which n = pq for distinct odd primes p....

6. Let n be any positive integer which n = pq for distinct odd primes p. q for each i, jE{p, q} Let a be an integer with gcd(n, a) 1 which a 1 (modj) Determine r such that a(n) (mod n) and prove your answer.
please do 7.19 7.20 and 7.21 7.19 Theorem (Quadratic Reciprocity Theorem and q be odd primes,...

please do 7.19 7.20 and 7.21 7.19 Theorem (Quadratic Reciprocity Theorem and q be odd primes, then Reciprocity Part). Let p (e)99 (mod 4) if p (mod 4) or q1 i p 3 (mod 4). (i)) (llint: Iry to use the techniquets used in the case of Putting together all our insights, the Law of Quadratic Reciprocity. we can write one theorem that we call Theorem (Iaw of Quadratic Reciprocity). Let p and q be odd primes, then if p...

Let p be an odd prime and a an integer with p not dividing a. Show that a(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)

Let p be an odd prime and a an integer with p not dividing a. Show that a(p-1)/2 is congruent to 1 mod p if and only if a is a square modulo p and -1 otherwise. (hint: think generators)
1. For n-pg, where p and q are distinct odd primes, define (p-1)(q-1) λ(n) gcd(-1-1.411) Suppose...

1. For n-pg, where p and q are distinct odd primes, define (p-1)(q-1) λ(n) gcd(-1-1.411) Suppose that we modify the RSA cryptosystem by requiring that ed 1 mod X(n). a. Prove that encryption and decryption are still inverse operations in this modified cryptosystem. RSA cryptosystem.
g(p+1)/2 (a) Suppose 9 is a p rimitive root of an odd prime p. Prove that- (mod p) g(p+1)/2 (a) Suppose 9 is a p rimitive root of an odd prime p. Prove that- (mod p)

g(p+1)/2 (a) Suppose 9 is a p rimitive root of an odd prime p. Prove that- (mod p) g(p+1)/2 (a) Suppose 9 is a p rimitive root of an odd prime p. Prove that- (mod p)

Let p be an odd prime. Prove that if g is a primitive root modulo p, then g^(p-1)/2 ≡ -1 (mod p).

Let p be an odd prime. Prove that if g is a primitive root modulo p, then g^(p-1)/2 ≡ -1 (mod p). Let p be an odd prime. Prove that if g is a primitive root modulo p, then go-1)/2 =-1 (mod p) Hint: Use Lemma 2 from Chapter 28 (If p is prime and d(p 1), then cd-1 Ξ 0 (mod p) has exactly d solutions). Let p be an odd prime. Prove that if g is a primitive...
9.3. Exercise 9.2 asked you to determine the value of (p-1)! (mod p) when p is...

9.3. Exercise 9.2 asked you to determine the value of (p-1)! (mod p) when p is a prime (a) Compute the value of (m 1)l (mod m) for some small values of m that are no (b) If you know the val ue of (n -1)! (mod n), how can you use the value to definitely ber. prime. Do you find the same pattern as you found for primes? distinguish whether n is prime or composite?
P-1 mod 4, prove that Σ k ( )-0. Let p be an odd prıme. Suppose that p k=1

p-1 mod 4, prove that Σ k ( )-0. Let p be an odd prıme. Suppose that p k=1 p-1 mod 4, prove that Σ k ( )-0. Let p be an odd prıme. Suppose that p k=1

4. Use quadratic reciprocity to find a congruence describing all odd primes for which 5 is a quad...

4. Use quadratic reciprocity to find a congruence describing all odd primes for which 5 is a quadratic residue. 4. Use quadratic reciprocity to find a congruence describing all odd primes for which 5 is a quadratic residue.