#13 where n =. p e N.I 3. Prove that r= +1 (mod11. Find 7(n), o(n), X(n), µ(n), w(n), and ø(n) for the following integers•22502869366502.3•22!12. Det p = 17 and d be a divisor of ø(p). Determine (d) for each d. Lall divisors, d, of ø(p).13.) Calculate all the primitive roots of 41 and 26. S0Oわり… て切'の|1の)4. Demonstrate that 21 has no primitive root.sime2,3,5,7,11,2115. Let r be a primitive root of n. If gcd(a, n) = 1, then the smalles(mod n) is called the index of a relative to r, denoted by ind-to solve congruences. Consider the properties of indices (p. 164) a||8x* = 11 (mod 13)

(a) Consider a=41. Therefore: φa=φ41=411-410=40 Now φa=40 can be written as: φa=40=23×5. Therefore…

Answered: Calculate all the primitive roots of 41…

Math

Advanced Math

Calculate all the primitive roots of 41 and 26.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.8: Introduction To Cryptography (optional)

Problem 23E

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Question

#13

where n =
. p e N.
I<u J!
Prove that if n is a perfect square, then X(n) = 1.
$ (n)
10/ Let r be a primitive root of some n > 3. Prove that r
= +1 (mod
11. Find 7(n), o(n), X(n), µ(n), w(n), and ø(n) for the following integers
•2250
286936650
2.3
•22!
12. Det p = 17 and d be a divisor of ø(p). Determine (d) for each d. L
all divisors, d, of ø(p).
13.) Calculate all the primitive roots of 41 and 26. S0
Oわり… て切'の
|1の)
4. Demonstrate that 21 has no primitive root.
sime
2,3,5,7,11,21
15. Let r be a primitive root of n. If gcd(a, n) = 1, then the smalles
(mod n) is called the index of a relative to r, denoted by ind-
to solve congruences. Consider the properties of indices (p. 164) a
||
8x* = 11 (mod 13)

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