Find all primitive roots: (a) modulo 25, or show that there are none (b) modulo 34,...

Find all primitive roots:

(a) modulo 25, or show that there are none

(b) modulo 34, or show that there are none

(c) Assuming that 2 is a primitive root modulo 67, find all primitive roots modulo 67.

Expert Solution

Colby Messinger answered 2 years ago

Find a primitive root, for all positive integral m, modulo each integer below. (a) 7m (Hint:...

Find a primitive root, for all positive integral m, modulo each integer below. (a) 7m (Hint: Using Corollary 5.15, find a common primitive root r modulo 7 and 72• The proof of Proposition 5.17 then guarantees that r is a primitive root modulo 72 for all positive integral m.) (b) 11m (c) 13m (d) 17m

Find a primitive root modulo 2401 = 7^4. Be sure to mention which exponentiations you checked...

Find a primitive root modulo 2401 = 7^4. Be sure to mention which exponentiations you checked to prove that your ﬁnal answer is indeed a primitive root. (You may use Wolfram Alpha for exponentiations modulo 2401, but you may not use any of Wolfram Alpha’s more powerful functions.)

Find all distinct roots (real or complex) of z2+(−6+i)z+(25+15i). Enter the roots as a comma-separated list...

Find all distinct roots (real or complex) of z2+(−6+i)z+(25+15i). Enter the roots as a comma-separated list of values of the form a+bi. Use the square root symbol '√' where needed to give an exact value for your answer. z = ???

Find all roots of the equation z^5=i, i.e. find the five values of i^1/5 and show...

Find all roots of the equation z^5=i, i.e. find the five values of i^1/5 and show them on an Argand diagram. Show all working

7. (16 pts) a. Show that 11 is a primitive root of 13. b. What is...

7. (16 pts) a. Show that 11 is a primitive root of 13. b. What is the discrete logarithm of 4 base 11 (with prime modulus 13)?

Compute φ(21). Find all the units modulo 21 and write down their inverses.

Find a primitive root for: (a) n = 18, (b) n = 50 (c) n =...

Find a primitive root for: (a) n = 18, (b) n = 50 (c) n = 27, (d) n = 625.

Find all the six roots of z = 16−16 sqrt (3i).

Roots of a complex number Find all the solutions to the equation (a) z^ 4 −...

Roots of a complex number Find all the solutions to the equation (a) z^ 4 − 1 = 0 (b) z ^5 + 2^5 i = 0 (c) z^ 6 − 16z^ 3 + 128 = 0

What is a strategy for handling a confounder? a) None of the above b) Enroll all...

What is a strategy for handling a confounder? a) None of the above b) Enroll all patients and stratify the data c) All of the above d) Enroll only patients that report no exposure to the confounder e) Enroll only patients that report exposure to the confounder

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