Given |a,b,c,n €Z, show that, if ac bc (mod n), a = b (mod), d= mdc(c, n). then

Q: Let x E Z and y E Z. Prove the following statement: If y = 2 mod 4, then xy 1 mod 4.

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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: Problem MCD = Greatest common divisor (GCD) t them.a, b, c and m €Zsuch that m 22. a-). Prove that a…

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Q: If cy (mod n) andc>0 then a) x= y (mod cn) b) x y (mod n) ) xy d) (mod") None of these

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Q: If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b = c (mod n) (b) b2 =…

A: We use the properties of congruences to answer the given question.

Q: If a cy (mod n) and c> 0 then a) x y (mod en) b) x y (mod n) ) x=y (mod) d) None of these :Select…

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Q: If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b3 c (тod n) (b) b2 =…

A: Given below the detailed solution

Q: If al = b (mod p), then prove that a = b (mod p).

A: (ii) given that                                                ap≡bp   (mod p) we have to prove…

Q: 3. Find the following: A. 3^0 mod 5 1 B. 3^1 mod 5 3 C. 3^2 mod 5 1 D. 3^3 mod 5 4

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Q: 15 Composite Then and O modn Show that if n there are with X#0 od n and y7 but where yy= Omod n.

A: Given n is a composite number

Q: Prove that's is prime p, then (a + b)² = (a² + b²)(mod p), Va; b € Z

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Q: and (mod 18), calculate (17)(49°. (496 –76+1) (mod 19)

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Q: If x = y (mod n) and u = v (mod n) then which of the following is true (a) x + u = y + v (mod n) (b)…

A: Given that x≡y (mod n) and u≡v (mod n)

Q: Let a, b, c and meZ, and m 2 2 1. Prove: if a =b (mod m), then GCF (a, m) = GCF (b, m) %3D m 2.…

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Q: a) If a| (21b−c) and 6c≅3b(mod2a), then a| 41c b) If a≅b(modc) and d|c then ?≅?(mod?) c) ∴(d|…

A: this is a question of modular arithmatic.

Q: 9 The residue of 6 (mod 5) is (Round to the nearest whole number.)

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Q: 4 If a = b (mod n), then a" = b™ (mod n) for every positive integer m.

A: It is given that  a≡b (mod n), then am≡bm (mod n) for every positive integer m. It will prove by…

Q: IfOcy (mod n) and e> 0 then a) *= y (mod cn) b) x= y (mod n) ) x=y (mod) d) None of these :Select…

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Q: 75 (mod 46)

A: Take a number and modulo with 46

Q: Recall that a = b( mod n) if a = b+ kn for some integer k. Use this to prove that if a = b ( mod n)…

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Q: Let 2,y EZ and nEN. Find which is true ot false. Show your answer with proof or counter example (if…

A: a) It is true Given x≡y(mod n)So, we've x = y + nk for some k∈ℤConsider gcd(x,n) = a , and gcd(y,n)…

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

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Q: Suppose gcd(a, n) = 1. Then a(") = 1 (n

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Q: If a = b (mod n) and b = c (mod n) then which of the following is true. (a) a = c (mod n) (b) a? =…

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Q: Let a,b,and c be natural numbers and n be a natural number > 0. Prove that if a = b mod n, then a^c…

A: Use mathematical induction to prove the given statement.

Q: If a = b (mod n) and a = c (mod n) then which of the following is true. (a) b = c (mod n) (b) b2 =…

A: We know that the property of congruence

Q: C 1 a b (b²+ c²) mod 2 = ?, a, b, c EN - {0}

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Q: 10 =1 (mod 9) Select one: O True O False

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Q: If nez then I89?bmodm a=+b moad m

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Q: O Find 5675 (mod 19

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Q: Ifx= y (mod n) and u =v (mod n) then which of the following is false. (a) x+u= y+ v (mod n) (b) хи в…

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