Christians who use the the Revised Common Lectionary have their daily liturgies alternate between year 1 (years ending in an odd number) & year 2 (years ending in an even number) and their Sunday liturgies alternate on a three year cycle year A (year 1 mod 3), year B ( year 2 mod 3), and year C ( 0 mod 3). What is the the year mod 6 that is simultaneously year 1 and B?

Q: 99999 9999 =9 (mod 10) Select one: True False

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Q: Any number n is congruent to the sum of its digits modulo 4. Select one: True False

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Q: If m is an integer, and if (m mod 11) = 6, then what is (5m mod 11)? 2 4 11

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Q: Find the value of x in the following: 25 mod 7 =  x 8 mod 12 = x -13 mod 7 =

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Q: The prime number 8191 is a None Inverse of 7 modulo 11 Carmichael umber Mersenne prime mmber

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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: Use Euler's Theorem to find 3112 (mod 23) None of the choices 3112 = 2(mod 23) This option O This…

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Q: If a= b (mod n) and gcd (a, n) = d, then gcd (b, n) = d :Select one True False

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Q: 2. If x mod 5 = 4, then x could be O 571 O 400 O 633 O 719

A: Given               x(mod 5)=4

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A: Given b mod 12= 7  To find 8b mod 12

Q: Give an odd prime p congruent to ±1 modulo 12. Show that (3) = 1.

A: Please see the attachment

Q: Find (853 mod 79)4 mod 27

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Q: (-130 mod 20·265 mod 20) mod 20 ?

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Q: What is the closest prime p following 123456 that satisfies p=3 (mod 4)

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Q: 5- If a = b mod (n), then ac = bc mod (n). 6- If a = b mod(n), then ak = bkmod(n) for every positive…

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Q: Where would 129 be on a mod 13 clock (which goes from 0 to 12)? What is the remainder…

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Q: Consider 3 · 1, 3 · 2, 3 · 3, . . . , 3 · 12 all mod 13, or in other words, the multiples of 3 in…

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Q: Suppose b is any integer. If  b mod 12 = 5,  what is 6b mod 12? In other words, if division of b by…

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Q: What is the value of o(5400 mod 13)

A: From Fermat's Theorem we know that if p is a prime number and p/a, a∈Z  then ap-1≡1(mod p) Since,…

Q: What prime numbers are squares in mod 17? (Include primes that are larger than 17). What primes p…

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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…

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Q: The prime number 8191 is a None Mersenne prime number Carmichael number Inverse of 7 modulo 11

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Q: x is congruent to 43 mod 12. Then x is None of the option 89 91 75

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Q: Find all solutions mod 31 to the congruence z = -5 (mod 31).

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Q: Is it true that 90 ≡ 64 (mod 13)?

A: As given equation 90≅64(mod 13) is False.

Q: Determine what number the product is congruent to in mod 3. 5.8 5.8 = (mod 3 )

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Q: 10. Use Euler's Theorem to show that 516) = 1 (mod 16).

A: Euler's theorem states that          "If gcd(a, n) = 1, then aφ(n) = 1 (mod n)

Q: Given any odd prime p, prove that: 2(p−3)! ≡−1 mod p. (Hint: Start with 2(p−3)!≡x mod p. Then work…

A: Let p be any odd prime number.  So we start with  2p-3!≡x mod p Also we have p-2≡-2 mod pp-1≡-1 mod…

Q: Show that if p and q are distinct primes, then pª-1 + q®=1 = 1 (mod pq).

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Q: determine what number the sum is congruent to in mod 3, 6+4 = __ (mod 3)

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Q: Prove the following results. (I). If n = 2(mod 4), then n is the sum of three squares of integers.…

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Q: Is 17 congruent to 4 modulo 6.

A: 17, when divided by 6, leaves remainder 5

Q: Find  mod (59, 10) and div (59, 10).

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Q: To Determine the value that 46 is congruent to IN modulo 7

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Q: The prime factorisation of 2021 is 2021 = 43 - 47. Determine the number of solutions to the…

A: Given that x2≡49    mod 2021 Also, 2021= 43 ·47

Q: III. Determine the value of a such that: 10. a = 11 (mod 21) and 90 s a s 110 11. a = 19 (mod 29)…

A: The given questions are related to congruences. The solution is explained below.

Q: (c) For all integers a and b, if a · b = 1 (mod 6), then a =1 (mod 6) or b = 1 (mod 6). (d) For all…

A: (c) The statement is false. For example take a=5, b=5 ab=2525≡1 mod(6) Hence ab≡1 mod(6) But a≡5…

Q: Use the Euler Theorem to calculate 17^81(mod 55)

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Q: Consider the equation 2x + 1 = 0 mod n. For which n are there no solutions? one solution? multiple…

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Q: 23. Let a,be Z and n eN. If a =b (mod n), then a = ab (mod n). (24, If a b (mod n) and c=d (mod n),…

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Q: The order of 5 mod 17 is *

A: Since ϕ(17) = 16 Therefore order can be the divisor of 16 So the order can be 1,2,4,8 or 16

Q: Calculate the following: 224 (mod 9) = ?

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Q: A.)Many printed airline tickets contain a 10-digit document number followed by a check digit. The…

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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: mod 32, given Xo=1 Please answer w

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Q: (a) What is 84 (mod 9)? (b) What is 52 (mod 5)? (c) What is -4 (mod 10)?

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Q: Compute 22 mod 3, 24 mod 5, 26 mod 7.  What do you notice?  Does Fermat predict your answers? (If…

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Q: 8. a = 20 (mod 31) and -15 s as 15.

A: As per the guidelines I am supposed to answer the first question only . For the other questions…

Q: 2. Suppose that instead of proving the claim "there is no integer n such that n= 2 mod 6 and n7 mod…

A: consider an integer n=26 such that n mod 6=26 mod 6               =2 mod 6 also, n mod 9=26 mod 9…