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...

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

Prove that "congruent modulo 3" is an equivalence relation on Z. What are the equivalence classes?

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 )

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