find the order of 3 modulo 29

Expert Solution

Colby Messinger answered 1 year ago

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.

Find ? as a function of ? if 81?″−90?′+29?=0, ?(3)=8,?′(3)=1 y=?

a) Suppose that a ∈ Z is a unit modulo n. Prove that its inverse modulo...

a) Suppose that a ∈ Z is a unit modulo n. Prove that its inverse modulo n is well defined as a residue class in Zn, and depends only on the residue class a in Zn. b) Let Z × n ⊆ Zn be the set of invertible residue classes modulo n. Prove that Z × n forms a group under multiplication. Is this group a subgroup of Zn? c) List the elements of Z × 9 . How many...

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

Find the order of each of the following elements. ( 3 , 4 ) in Z...

Find the order of each of the following elements. ( 3 , 4 ) in Z 4 × Z 6 ; ( 6 , 15 , 4 ) in Z 30 × Z 45 × Z 24; ( 5 , 10 , 15 ) in Z 25 × Z 25 × Z 25; ( 8 , 8 , 8 ) in Z 10 × Z 24 × Z 80.

Describe in behavioral VHDL a modulo-m up/down counter with the following interface: – Generics • Modulo...

Describe in behavioral VHDL a modulo-m up/down counter with the following interface: – Generics • Modulo base (m with default value of 16) – Inputs Clock (clk  1 bit) Asynchronous reset (rst  1 bit) Counting direction (up_down1 bit) – 1Counting up – 0Counting down – Outputs 2 – Run behavioral simulation • Count value (count • In Vivado – Create a project   bits)

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 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 the order of growth for the following function ((n^3) − (60n^2) − 5)(nlog(n) + 3^n...

Find the order of growth for the following function ((n^3) − (60n^2) − 5)(nlog(n) + 3^n )

Prove: There are inﬁnitely many primes congruent to 3 modulo 8. Hint: Consider N = (p1p2···pr)2...

Prove: There are inﬁnitely many primes congruent to 3 modulo 8. Hint: Consider N = (p1p2···pr)2 + 2.

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