Question

Let p be an odd prime of the form p = 3k+2. Show that if a^3...

Let p be an odd prime of the form p = 3k+2. Show that if a^3 ≡ b^3 (mod p), then a ≡ b (mod p). Conclude that 1^3,2^3,…,p^3 form a complete system of residues 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, 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.
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 an odd prime and let a be an odd integer with p not...
Let p be an odd prime and let a be an odd integer with p not divisible by a. Suppose that p = 4a + n2 for some integer n. Prove that the Legendre symbol (a/p) equals 1.
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.
Show that the numbers 1, 3, 3^2 , . . . , 3^15 and 0 for...
Show that the numbers 1, 3, 3^2 , . . . , 3^15 and 0 for a complete system of residues (mod 17). Do the numbers 1, 2, 2^2 , . . . , 2^15 and 0 constitute a complete system of residues (mod 17)?
4. Prove that if p is a prime number greater than 3, then p is of...
4. Prove that if p is a prime number greater than 3, then p is of the form 3k + 1 or 3k + 2. 5. Prove that if p is a prime number, then n √p is irrational for every integer n ≥ 2. 6. Prove or disprove that 3 is the only prime number of the form n2 −1. 7. Prove that if a is a positive integer of the form 3n+2, then at least one prime divisor...
et P be an odd prime number. Suppose there are two natural numbers A, B such...
et P be an odd prime number. Suppose there are two natural numbers A, B such that 2P = A2 + B2. Show that A, B are odd and coprime. Show that P ≡ 1 (mod 4). Write P as a sum of two squares of natural numbers. Find a Primitive Pythagorean Triple (U, V, P).
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.
Let b be a primitive root for the odd prime p. Prove that b^k is a...
Let b be a primitive root for the odd prime p. Prove that b^k is a primitive root for p if and only if gcd(k, p − 1) = 1.
If p = 2k − 1 is prime, show that k is an odd integer or...
If p = 2k − 1 is prime, show that k is an odd integer or k = 2. Hint: Use the difference of squares 22m − 1 = (2m − 1)(2m + 1).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT