Question: Let p be a prime with p 1 (mod 4), and b := ((p 1)/2)!. Show that b^2 1 (mod p).

Let p be a prime with p 1 (mod 4), and b := ((p 1)/2)!. Show that b^2 1 (mod p).

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

Let p be a prime satisfying p 3 (mod 4). Let p be a prime satisfying p = 3 (mod 4). (a) Let a be a quadratic residue modulo p. Prove that the number b = a^p + 1/4 (mod p) has the property that b^2 =...

Q:

Please answer and explain both 7.58 and 7.59. Thank you! EXERCISE 7.58. Let n pq, where p and q are distinct primes. Show that we have a ring isomorphism Zn(X] Zp(??? ????] EXERCISE 7.59. Let p be a...

Q:

The subject is discrete math, one of the subjects on the advanced math. This is all I was given. I`m working on these problems too, and expecting the expert-answers by the time I finish, so that I...

Q:

1. Assuming that xy=x+y+1 and xy = xy +x+y are two binary operations defined for all x, y ER, i) prove that both and are commutative; ii) prove that both and are associative; iii) prove that is...

Q:

{2) (a) Let p be a prime number. Define \"primitive root modulo p.\" (b) If g is a primitive root modulo p and a is an integer such that geda, p) = 1, define the discrete logarithm of a with respect...

Q:

7.1 Let f (x) = 4 x 2 ; and let P be a partition of [0; 1] given by P = 0; 1 n ; 2 n ; ; n1 n ; 1 ; n 2 N:: Find U (P) and L(P) with respect to this partition P. 7.2 Obtain also the values U (P) and...

Q:

7.1 Let f (x) = 4 x 2 ; and let P be a partition of [0; 1] given by P = 0; 1 n ; 2 n ; ; n1 n ; 1 ; n 2 N:: Find U (P) and L(P) with respect to this partition P. 7.2 Obtain also the values U (P) and...

Q:

Primes and Probability. In this problem, you will use the following facts: (1) any integer can be uniquely factored into primes; (2) the number of primes less than any number m is (m/log m) (this is...

Q:

A fact you should use. Let p be a prime. Then Zp has a generator. Namely g Zp whose powers give all the group. Zp = {1,g,...,gn2}. In particular all the different powers of g give different numbers....

Q:

7. Primes and Probability. In this problem, you will use the following facts: (1) any integer can be uniquely factored into primes; (2) the number of primes less than any number m is (m/log m) (this...

Q:

Calculate the value of a six-month futures contract on a Treasury bond. You have the following information: (Do not round intermediate calculations. Round your answer to 3 decimal places.) Six-month...

Q:

Prior to adjustment at the end of the year, the balance in Trucks is $182,600 and the balance in Accumulated DepreciationTrucks is $74,950. Details of the subsidiary ledger are as follows: a....

Q:

Which of the following allocations is most likely to meet the substantial test in the substantial economic effect rules? ( A The ROY LLC specially allocates $ 2 0 , 0 0 0 of income each year to...

Q:

(a). The capital budget should be consistent with the firm's: A. historical growth in sales. B. strategic plans C. current level of debt. D. dividend policy (b). Which one of the following would not...

Q:

6. Have you used solid reasoning in your argument?

Q:

8. Have you checked (and rechecked) your speech for logical fallacies? Have you addressed and removed any that youve identified?

Q:

3. Have you assessed your audiences disposition and needs? Have you considered what is most relevant to them?