n=23 satisfies one of the following congruence 24 + 27 =5+2 (mod n) O. 24 x 27 =5 (mod n) 24 + 27 =5 (mod n) 24 - 27 =5 (mod n)

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: As per the question we have to solve the following polynomial congruence equation : x3 + x2 + 3 ≡ 0…

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: Why do Christmas and New Year's Day always fall on the same day of the week? O 25 ( mod 7) = 31 (…

A: To explain why Christmas and new year's day always fall on the same day of the week.

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

A:

Q: 1. Find all solutions (a) 2x + 3 = 7 (b) 2x + 3 = 7 to the following congruences.. (mod 9) (mod 20)

A:

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: 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: True or False : a – c ≡ b – c (mod n) ⟺ a ≡ b (mod n)

A: We have to solve given problem:

Q: n=23 satisfies one of the following congruence 24 + 27 =5+2 (mod n) 24 - 27 =5 (mod n) 24 x 27 =5…

A: Fourth option is correct

Q: If a =b (mod m) and a = b (mod n) then a = b (mod m+n) Select one: O True O False

A:

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…

A:

Q: Find all solutions of each congruence and explain why these are all the solutions. (It is possible…

A:

Q: n=23 satisfies one of the following congruence 24 - 27 = 5 (mod n) 24 x 27 = 5 (mod n) 24 + 27 = 5+…

A:

Q: Find the common solutions to the congruences 2x 3x 4x 1 (mod 5) 9 (mod 6) 1 (mod 7).

A: Given : 2x≡1 (mod 5)3x≡9 (mod 6)4x≡1 (mod 7) To find : The common solutions to the congruences. For…

Q: 2221 (mod 13) is equal to O 10 (mod 13) O 1 (mod 13) 7 (mod 13) 6 (mod 13) O None of these

A:

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

A:

Q: If x = 2 (mod 5) and y = 4 (mod 5) then 2x – 3y =? (mod 5)

A:

Q: On their anniversary, Luna received a box containing x violet flowers. The number of these flowers…

A:

Q: If a = b (mod n) and b =c (mod n) then which of the following is false. a = c (mod n) a = c3(mod n)…

A:

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

A:

Q: 2x = 4 (mod 8) a. has no solution b. has infinite solutions c. has a unique solution modulo 8 which…

A: Here 2x≡4 (mod 8). Hence 2x=4+8k, for some integer k. Dividing by 2, x=2+4k, for some integer k.…

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

A:

Q: Hanb(mod n) and b c(mod n) then which of the following is trae. (a) anc (mod n) () 2=c(mod n) (c)…

A:

Q: Determine if x² = 29 mod 541 has a solution.

A:

Q: The equation 15x=30 (mod 50) has: 5 non-congruent solutions modulo 50 6 non-congruent solutions…

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Q: QUESTION 2 Which is correct? 72+ 5 = 32 (mod 9) 74 = 164 (mod 10) 19× 27 = 7– 3 (mod 6) 24 – 27 = 5…

A: 72 + 5 = 49+5             = 54             = 9 (mod 9)             = 32 (mod 9) Hence 1 is true. 7 4…

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

A:

Q: Show that if a is an even integer then a² = 0 (mod 4) and if a is odd integer then a² = 1 (mod 4)

A: We know that an even number is a multiple of 2 and we write an even number k as k=2m for some…

Q: (b) Give an example of a composite integer n such that the congruence x =1 (mod n) pas more than two…

A:

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

A:

Q: Assume all variable as positive integers. Given and a-2n+2 (mod 7) 000 b = 3n+1 (mod 7) Which of the…

A:

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: In the question we are given the following polynomial congruence equation : x3 + x2 + 3 ≡ 0 (mod…

Q: Consider the congruence a² + x + 1 = 0 mod 21. Solutions to the congruence above must also be…

A: The given congruence equation is .We will solve this congruence relation using the Chinese remainder…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.