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?

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: 2-) Find all in tegers x such thet 5x = 12 (mod 7) 10x = 4 (mod 1) 7x E 16 (mod 10d ond 1occ < x <…

A: Given: 5x≡12(mod 7) 10x≡4(mod11) 7x≡16(mod 10) and 1000≤x≤3000

Q: 9. Let a and b be integers. Prove that if a =7 (mod 8) and b = 3 (mod 8), then: (a) a + b = 2 (mod…

A: Your questions solution below in images

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: For each statement, indicate whether it is true or false. Then prove or disprove it. (a) For all SC…

A: (a) FALSE.  Consider S ⊆ℤ, defined by  S = { 2+8k | k ∈ℤ } U { 2+12r | r∈ℤ }.  Then the given…

Q: 2= 12 mod 2 - - 2 = 11 mod 18 20 = -2 mod 19 - 2= 20 mod 2 - -17 = 20 mod 8 6.7 = -14 mod 11 - -1 =…

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Q: (-130 mod 20·265 mod 20) mod 20 ?

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Q: X=2 (mod 10), X=2 (Mod 8), x=o (Mod 6) What is the smallest positive number ?

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Q: x = 2 (mod 5) 2r = 22 (mod 8) 3x = 12 (mod 21) (i) How many solutions does it have lying between 0…

A: i)Given thatNotice first that the moduli are pairwise relatively prime, Therefore, we can use the…

Q: 1. For each solution: determine weather there is a a congruence a x² = -1 (mod 397) b.) x²+8x+14=0…

A: 1a) To determine whether the congruence equation x2 ≡ -1 (mod 397) has a solution, we need to check…

Q: 1. Solve the Congruence x^5 ≡ 2 (mod 7)   2. Solve the congruence x^7 ≡ 10 (mod 23)   Show work…

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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

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

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Q: 1. A+B (mod 173) 2. C-D (mod 432) 3. 23 x E (mod F) 4. G+5 (mod 7) АВМ 1А A B C E F G Hannah 7550…

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Q: Identify if the given statement is true or false: I. If a is an integer, the (a^2 is congruent to 0…

A: Given some statements. Check whether these statements are true or false.

Q: Rewrite in exponential form Log4 1024 = 5 graph of - امي 100 pil H - Z Of = 5 state the asymptotesy…

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Q: Determine the number of primitive roots modulo 23.

A: Solution

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

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

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

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Q: If 19 =7 (mod 6) and 27 =3 (mod 6) then 19x 27 = 7+3 (mod 6) 19+27 = 7+3 (mod 6) 19+27 =7x 3 (mod 6)…

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Q: Does 5x = 6 mod 12 have a solution? How many?

A: As per our guidelines we are supposed to answer only One question  if there are multiple questions…

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: Ques 3. Verify the following statements. 1. 55 - 26 = (3 - 2) (mod 4) 2. 55 - 26 = (3 - 2) (mod 4)…

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Q: 20.What is the value of n such that (24  is congruent to 58 mod n) ? a.13 b.17 c.-34 d.-13

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

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: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

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: which one will give a solution of [6,13] a)4x is identical to 3 mod 7 b)9x is identical to 11 mod…

A: which one will give a solution of [6,13]

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

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

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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…

Q: In the congruence equation 3x + 12 = mod 10, which of the following is FALSE O a. 5, 15, 25, 35,..…

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Q: In the following question: " Let a, b ∈ Z. Show that if a ≡ 5 (mod 6) and b ≡ 3 (mod 4), then 4a +…

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