Answer the following: Is a = y( mod 5) reflexive? [Select] [Select Yes Is a = y( mod 5) symmetric No Is a = y( mod 5) anti-symmetric? [Select] Is a = y mod 5) transitive? Select]

Q: The statement a ≡ b (mod n) is called a congruence.

A: Given that  The statement a ≡ b (mod n) is called a congruence.

Q: Show that if a and b are integers and m and n are positive integers such that n|m, then If a = b(mod…

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Q: Q. Now make a multiplication table for modulo 3. ol 1 2 IN 0 1 2

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: Let m be fixed positive integer. Then an integers a is congruent to an integer b modulo m, if: ab|m…

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Q: - Calculate the orders of 2 (mod 67) and of 2 (mod 73).

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Q: {X = I (mod 3) 2X= 2 (mod 5)

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Q: Prove for any integers a and b, if (a3+b3) mod 3 is not 0, then (a+b) mod 3 is not 0. (Hint: recall…

A: Congruence Modulo Relation on Integers: Let a, b∈ℤ and let m be a fixed positive integer.  Then a…

Q: Let a and b be integers satisfying a=3(mod 11) and b=8 (mod 11). If c=3a+4b then None of these c=9…

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Q: The notation x = y mod n is used to indicate the unique integer x in the range 0 :$ x < n such…

A: Given statement is that the notation x = y mod n is used to indicate the unique integer x in the…

Q: . Determine whether or not x³ + 2x + 1 and x4 + 3x - 2 are congruent mod (x² + 2x + 2) in Q[x].

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Q: Compute 21200 mod 27.

A: To Find: 21200mod 27

Q: 2. If a = 1 (mod p), then a=1 (mod p). Select one: True False

A: If , then . The truthfulness of the given statement can be proved by taking an arbitrary value for…

Q: Let x E Z. Prove that either x2 = 0 (mod 4) or x2 = 1 (mod 4).

A: By the help of even and odd integer's we prove the result. The answer is given as follows :

Q: Prove that the order of 3 modulo 19 is a divisor of 18.

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Q: If a ≡ b (mod n1) and a ≡ b (mod n2), must it be true that a ≡ b (mod n1 + n2)? Either give a proof…

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Q: 355 ( mod 7) + 234 ( mod 7)

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Q: Which expression is equivalent to [77 · (-65) + 147] mod 7? O 7 O [(147 mod 7) · (-65 mod 7) + (77…

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Q: Which of the following is true? a. 24 = 3 (mod4) b. 56= 4(mod5) c. 62 = 4(mod4) d. 58 = 3 (mod5) Oa…

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Q: Determine which of the following statements are true: a. 54=72(mod16)

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Q: Use a Proof by Contradiction to prove that there is no integer a such that a congruent 5 (mod 14)…

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Q: Show that there are exactly (p−1)/2 nonzero squares mod p.

A: To prove that there are exactly p-12 nonzero squares mod p.

Q: Select the following statements that are true. 261000 = 1 (mod 3) (2022) 10 (FC6) 16 In Z6, 2¹⁰ = 2…

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Q: Show that for any positive integer x, at least one of x, x+ 2, or x+ 4 is divisible by 3

A: The objective is to show that for any positive integer x at one of x, x+ 2, or x+ 4 is divisible by…

Q: 2. Prove that if a = b( mod r) and c = d( mod r) then a – c= b – d( mod r)

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Q: Prove that if a = b (mod m) and if c = d (mod m), then ac = bd (mod m).

A: a≡b   (mod m)⇒ m|(a−b)That is there exist an integer k such that a−b=mk

Q: For which positive integers a is the congru

A: Given,               ax4≡2 (mod 13)

Q: Consider the congruence 9x   21 (mod 33). (a) Does 9 -1(mod 33) exist? Explain why or why not.

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Q: Prove by any method(contradiction/contrapositive or cases)   Prove that (a mod 2)(b mod 2)= (ab)…

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Q: 2. Prove that for any m = 1 mod 11 that there are no integer solutions of m = 2r" - 9y.

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Q: Which value of x satisfies x= 233 (mod 7)? O 495 o 699 o 424 o 352

A: 352

Q: 16. Prove that an integer (a,-1an-2 · . . ao)10 is divisible by 11 if and only if ao + a2 + a4 + . .…

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Q: he smallest positive integer x such that x = 22 (mod 25), x =

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Q: 10. Prove that a³ =a (mod 6) for every integer a.

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Q: Ha = b (mod n) and gcd (a,n)= d, then gcd (b,n) %3D

A: Given a≡b(mod n). This can be written as a-b≡0(mod n). Implies a-b=kn for some natural number k.…

Q: Let a and b be integers and n a positive integer. Assume also that a and n have a common divisor d…

A: Use the following concepts, to prove the required result. If a divides b then b is a multiple of a.…

Q: Determine all solutions x ∈ Z to the triple x ≡ 5 (mod 6), x ≡ 7 (mod 10) and x ≡ 2 (mod 15) of…

A: We reduce the congruence and then solve

Q: Which of the following satisfies the congruence 3x O O 2 T - 2 (mod 5)?

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