Question: Let n E T. Prove: If p is an odd prime divisor of 1/12 + 1, then p E 1 (mod 4). (Hint. Note that

Let n E T\". Prove: If p is an odd prime divisor
Let n E T\". Prove: If p is an odd prime divisor of 1/12 + 1, then p E 1 (mod 4). (Hint. Note that n2 E -1 (mod p). So, what is the order of n mod p? What does Theorem 27 say about the relationship of the order to 4309)?)

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 Mathematics Questions!

Q:

MATH 135 S 2016: Assignment 9 Solutions 1. Prove that for any integer n, 441n43 + 374n35 + 285n23 0 (mod 55). Solution: Since 55 = 5 11 and gcd(5, 11) = 1, we may use the Splitting Modulus...

Q:

1) We have shown that if p is a prime number then for all a, a p = a mod p (Fermat). Hence if there exists a such that a p 6= a mod p, then p is a composite number (not a prime). Use this to show 231...

Q:

1) We have shown that if p is a prime number then for all a, a p = a mod p (Fermat). Hence if there exists a such that a p 6= a mod p, then p is a composite number (not a prime). Use this to show 231...

Q:

Need d) & e) Consider the elliptic curve E given by the equation y2-x3-x defined over the real numbers. Tet F(R.) denote its set of points. (a) Draw a picture of E(R). If P is the point (0,0) i E(R),...

Q:

1) We can design a MAC function that generates MAC tags as follows: Select one: a. All the options b. Use AES or 3DES in CFB mode c. Use a hash function along with a secret shared key d. Use AES or...

Q:

1) We can design a MAC function that generates MAC tags as follows: Select one: a. All the options b. Use AES or 3DES in CFB mode c. Use a hash function along with a secret shared key d. Use AES or...

Q:

Math 311W Problem Set 5 Due Friday, October 16, 2015 1. Find the prime factorizations for 51 and 198, and use your answers to nd the gcd of 51 and 198. (No proof is required here, just write down the...

Q:

1) We can design a MAC function that generates MAC tags as follows: Select one: a. All the options b. Use AES or 3DES in CFB mode c. Use a hash function along with a secret shared key d. Use AES or...

Q:

Proof: Let p be an odd prime. Then p is a sum of 2 squares if and only if p = 4k + 1 for some k ? N. hint: ? This is where the action happens. By the division theorem, we know that every odd prime...

Q:

Suppose p is an odd prime and a QR p . Show that: (a) p 1 (mod 4) a QR p . (b) p 3 (mod 4) a QR p Hints: When is even/odd? When is 1 QR p ? (Q => Rational Number, R => Real Number) . |A the number of...

Q:

The community is involved in promoting the development of all learners. Discuss.

Q:

A rock is suspended by a light string. When the rock is in air, the tension in the string is 39.2 N. When the rock is totally inunersed in water, the tension is 28.4 N. When the rock is totally...

Q:

Yurman Inc. uses a job-order costing system. During the month of May, the following transactions occurred: a. Purchased materials on account for $29,670. b. Requisitioned materials totaling $24,500...

Q:

You are the Marketing Director of a B2B Organisational Marketing company of your choice (your choice of company should be communicated to your lecturer and approved by week 6 of the semester). You...