Which are true for modulo 12? 1.) Does 5x ≡ 6 mod 12 have a solution? How many? 2.) Does 4x ≡ 6 mod 12 have a solution? How many? 3.) Does x^2+ 1 ≡ 0 mod 12 have a solution? How many? 4.) If xy ≡ 0 mod 12 does it follow that x ≡ 0 mod 12 or y ≡ 0 mod 12?

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Q: Za) Let A = {n E Z | n = 0 (mod 2)} and B = {n € Z | n = 0 (mod 4)}. Prove that if n E (A – B), then…

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A: Topic:- basic maths

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Q: 8, Suppose a,b € Z. Prove that a = (mod 5). b (mod 10) if and only if a = b (mod 2) and a = b

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Q: 2. Give an example to show that a (mod n). b (mod n) need not imply that a =b

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Q: 1. Show that an integer n is divisible by 2 if and only if its last digit is even. (Hint: For each i…

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Q: Suppose that p is a prime number. Given this information prove that if x is an integer such that x^2…

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Q: 4. (a) Solve the set of congruences х 1(mod 3), x= 2(mod 4), x = 3(mod 5).

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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: (a) Use cases based on congruence modulo 3 and properties of congruence to prove that for each…

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Q: whether 2 is a primitive root modulo 19. Please state the reason.

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Q: (b) Prove that if a = 7 mod 10 and b = 6 mod 15, then a + b = 3 mod 5.

A: Our objective is to prove . Since you have posted multiple questions I am solving one.

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: 29 is a primitive root modulo 38? True or False

A: The answer to this question is TRUE.

Q: Use the index system modulo 19 to find all solutions of x³ = 11 (mod 19) and 5ª = 4 (mod 19)

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Q: 25 Prove that mod 7 5 for all Gindegars and bin b mod 7-6

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Q: Solve the system of congruence's x = 2 (mod 3), x = 4 (mod 5), x = 1 (mod 7)

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Q: Q3/ Use Chinese theorem to solve the following congruence: X=2 mod 3 X=1 mod 5 X 2 mod 4

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Q: Use Wilson's Theorem to prove that for primes p congruent to 1 modulo 4 the quadratic congruence 1'…

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Q: The equation 21x = 49 (mod 77) has: O no solution modulo 77 only 7 non-congruent solutions modulo 77…

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Q: Determine four values of x that will satisfy: x ≡ 4 mod 5 & x ≡ 3 mod 7 please show your solution

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Q: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False

A: 12x ≡ 18 (mod 15) has exactly 3 distinct solutions modulo 15 Select one: True False