(5a) Let A = {n E Z | n = 2 (mod 3)} and B = {n E Z | n = 1 (mod 2)}. Prove that if n E (A n B), then n² = 1 (mod 12)

Q: Let a, be Z and n E N. For each statement decide whether it is necessarily true, or whether it can…

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Q: Show that 2 is a primitive root modulo 3" for all n > 1.

A: To prove that 2 is a primitive root modulo 3n for all n≥1.

Q: Find the smallest integer a > 1 such that a –1 = 2a (mod 11

A: To find:

Q: The remainder when a is divided by 7 is 2 and the remainder when b is divided by 7 is 5. (So a mod 7…

A: Given that remainder when "a" is divided by 7 is 2

Q: Show that (p-1)(p2) (pr) (-1)'r!(mod p), for r= 1, 2, . . . ,p - 1. .

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Q: Q3 Not submitted Section 4.1 # 14 Show that if a, b, and e are integers with e > 0 such that a = b…

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Q: Let n be a positive integer and let ged(b, n) = 1. Show that bx by (mod n) if and only if x=y(mod…

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Q: (b) By applying part (a), solve the congruences 2x = 1 (mod 31), 6x = 5 (mod 11) 3x = 17 (mod 29).…

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Q: 2. Let f: Z-Z be given by the following rule: x+6 x=0 x = 1 x+8 x 2 f(x)=x+5 (mod 3) (mod 3) (mod 3)…

A: The given function is, fx=x+6x≡0 mod3x+5x≡1 mod3x+8x≡2 mod3 To Find: (a) Example to show that f is…

Q: (a) Prove that 318 = q (mod 19).

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

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Q: Let a € Z be odd. (a) Prove that a = 1 (mod 4) or a = 3 (mod 4). (b) Prove that a² = 1 (mod 4).

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Q: (7) Let m≥ 1 and let R= {0, 1, 2,...,m - 1}. (a) Prove that if r1, T2 € R and r₁ r2 (mod m), then r₁…

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Q: Let A = {1, 2, ..., 12}. Let aRb mean a = b (mod 5). (a) Give [2]R. [3]R, and [5]R. (b) Give [2]…

A: A set of ordered pairs is referred to as a relation in the area of mathematics and computer science.…

Q: Let p be an odd prime number. Prove the following statements. (a) (7) = 1 if and only if p = 1, 3…

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Q: 4. Prove that if a = b (modn) and m|n, then a = b (modm)…....

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Q: Proposition 1.2. Say a = a' (mod m) and b = b' (mod m), then (i) a+b=a'+b' (mod m), and (ii) ab a'b'…

A: x=y (mod n)⇒ n|(x−y)That is  x−y=nk  for some integer k

Q: please do 7

A: (a) p is a prime number. Since,

Q: ove that n’ +5n is divisible by 6 for all n E N.

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