2. If a = 3 (mod 11) and b = 9 (mod 11), compute the values, positive and fully-reduced modulo the modulus: (a) Compute 2a + b (mod 11) (b) Compute (a - b)² (mod 11)

Q: (10) Find all solutions of the congruence 2 = 22 (mod 53). C

A: We shall be using primitive roots to solve this congruence.

Q: 1) Compute the order of a modulo 7 for a = 1,2,....6. Find all primitive roots modulo 7.

A: Order of the element

Q: Compute or show that it does not exist. (a) 149-¹ (mod 200); (b) 95-¹ (mod 323).

A: Please see the below picture for detailed solution.

Q: (6) Compute ind2 (19) modulo 101.

A: We recall the definition of a primitive root.

Q: (2) Compute the order of a modulo 11 for a = 1,2,..., 10. Find all primitive roots modulo 11.

A:

Q: SImalest posiuiy OI the n) is order of a modulo n. Find the additive orders of each of the following…

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Q: Show that if a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ b + d (mod m).

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Q: Podasip 11. If p is prime, then every c can be expressed as a sum of two squares: x² + y² = c(mod…

A: The given is statement is not accurate. The correct statement in connection with the given statement…

Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

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Q: Which of the following are true modulo 12? (1) Does 5z = 6 mod 12 have a solution? How many? (2)…

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Q: Compute (1001 mod d) for d = 2, 3,..., 10.

A:

Q: 13. Suppose that z1 V3 +i and z2 = 2/2+ 2v2i. 22 (a) Write z1 and z2 in mod-arg form. (b) Hence…

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Q: Show that: if a = b(mod n) and C = d\modn), then a +c =b+d\mod n)!

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Q: Exercise 3. 3x +1= 2 (mod 9) a has no solution modulo 9 b. has six non-congruent solutions modulo 9…

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Q: If n 2 1, then the Fermat number Fn 22" +1 is prime if and only if %3D 3(F.-1)/2 = -1 mod (Fn).

A:

Q: (f) If a = b (mod n), then a* bk (mod n) for any positive integer k.

A: