Question

Number Theory: Find a square root of −1 modulo p for each of the primes p...

Number Theory:

Find a square root of −1 modulo p for each of the primes p = 17 and p = 29. Does −1 have a square root modulo 19? Why or why not?

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
Find a square root of −1 modulo p for each of the primes p = 17...
Find a square root of −1 modulo p for each of the primes p = 17 and p = 29. Does −1 have a square root modulo 19? Why or why not?
For which primes p is 15 a square modulo p?
For which primes p is 15 a square modulo p?
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.
For each prime number p below, find all of the Gaussian primes q such that p...
For each prime number p below, find all of the Gaussian primes q such that p lies below q: 2 3 5 Then for each Gaussian prime q below, find the prime number p such that q lies above p: 1 + 4i 3i 2 + 3i
(i) Verify that 2 is a primitive root modulo 29. (ii) Find all the primitive roots...
(i) Verify that 2 is a primitive root modulo 29. (ii) Find all the primitive roots modulo 29. Explain how you know you have found them all. (iii) Find all the incongruent solutions to x6 ≡ 5(mod 29).
Let p and q be primes. Prove that pq + 1 is a square if and...
Let p and q be primes. Prove that pq + 1 is a square if and only if p and q are twin primes. (Recall p and q are twin primes if p and q are primes and q = p + 2.) (abstract algebra)
Given that 2 is a primitive root modulo 19, find all the primitive roots modulo, 19....
Given that 2 is a primitive root modulo 19, find all the primitive roots modulo, 19. You must know how you are getting your answer and make sure all your answers are in the canonical residue set
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square root of 17 is irrational too, for any natural number n. use the following lemma: Let p be a prime number; if p | a2 then p | a as well. Indicate in your proof the step(s) for which you invoke this lemma. Check for yourself (but you don’t have to include it in your worked solutions) that this need not be true if...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square root of 17 is irrational too, for any natural number n. use the following lemma: Let p be a prime number; if p | a2 then p | a as well. Indicate in your proof the step(s) for which you invoke this lemma. Check for yourself (but you don’t have to include it in your worked solutions) that this need not be true if...
Find the square root that is a real number.       negative StartRoot negative 4 EndRoot Select...
Find the square root that is a real number.       negative StartRoot negative 4 EndRoot Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. A. The real number square root is nothing . ​(Simplify your answer. Type an integer or a​ fraction.) B. The square root is not a real number.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT