Question

In: Advanced Math

Find a characterization of primes p such that 3 is a square mod p and then...

Find a characterization of primes p such that 3 is a square mod p and then prove it.

Solutions

Expert Solution


Related Solutions

find all primes p such that 6 is a square mod p? please with clear hand...
find all primes p such that 6 is a square mod p? please with clear hand writing
Find all primes p for which −5 is a quadratic residue.
Find all primes p for which −5 is a quadratic residue.
Prove f: Zmod p---> Z mod p is a ring homomorphism and find the kernel of...
Prove f: Zmod p---> Z mod p is a ring homomorphism and find the kernel of f.
Find the P(>3kids or ≥2cars). Find the P(>1car | 3-5kids).
QUESTION 1   Kids   Cars 1 2 3 4 5 6 Total 1 1 1 2 2 2 2 10 2 4 2 1 3 3 2 15 3 0 2 2 0 0 1 5 Total 5 5 5 5 5 5 30 Use the two-way table above to answer the following question.Find the P(>3kids or ≥2cars).   QUESTION 2   Kids   Cars 1 2 3 4 5 6 Total 1 1 1 2 2 2 2...
If p,p+2 are twin primes, prove 4((p−1)!+1)+p≡0 modp(p+2)
If p,p+2 are twin primes, prove 4((p−1)!+1)+p≡0 modp(p+2)
Q−3: [5×4 marks] a. Find a, b if a+2b=107 mod 9 and 2a+b=-55 mod 7. b....
Q−3: [5×4 marks] a. Find a, b if a+2b=107 mod 9 and 2a+b=-55 mod 7. b. Write the prime factorization of 229320 and 49140, hence find GCD and LCM. c. Convert the following number (1303)4 to base 5. d. Using the Prime Factorization technique determine whether 173 is a prime. e. Use the cipher: f(x)=(x+7) mod 26 to decrypt “THAO ALZA”.
Find the smallest positive integer x that satisfies the system of congruences x ≡ 3 (mod...
Find the smallest positive integer x that satisfies the system of congruences x ≡ 3 (mod 5). x ≡ 5 (mod 7). x ≡ 7 (mod 11)
find the polar presentation of (j-square root of 3)
find the polar presentation of (j-square root of 3)
Show that if a and b are integers with a ≡ b (mod p) for every...
Show that if a and b are integers with a ≡ b (mod p) for every prime p, then it must be that a = b
let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod...
let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod p), i.e., the number of elements (x,y), x,y=0,1,...,p-1, which satisfy x^2 - 2 y^2=1 (mod p)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT