3400 m is prime numbers, then compute 27 (mod m) 2. If m is natural numbers, show that a (mod m ) = b (mod m) if a = b (mod m) 3 If m is prime numbers, then show that M-1 mod ma 1+2+3+ + (M-2) + (m-1) mod m

Q: Please give detailed steps!

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

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Q: Find an integer n such that n = 1 mod 7, n = 3 mod 8, and n = 2 mod 9.

A: We can solve this system of congruences using the Chinese Remainder Theorem.

Q: if b is modulo m and a is another unit with a=b mod m, we say that d is the---------of a modulo m to…

A: As with such a large amount of concepts we are going to see, congruence is straightforward, perhaps…

Q: 1) Find 100147 + 147100 (mod 11)

A: Image is attached with detailed solution.

Q: If mx = 1 (mod n) has a solution, then nx = 1 (mod m) has no a solution. Select one: True False

A: We know the definition of Congruence ,  Suppose m be a positive integer , we say that integers a and…

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: Compute or show that it does not exist. (a) 149-¹ (mod 200); (b) 95-¹ (mod 323).

A: Please see the below picture for detailed solution.

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: Take p and q are primes and p=3mod4 and q=3mod4. Take n=pq such that an integer z has a square root…

A: Given that р and q are primes and p=3mod4 and q=3mod4.

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

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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: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101  To find: Number of solutions that exists. Method Used:  For any, xk≡b mod p,…

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

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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: (a) Show that, for any odd prime p > 5, 1 if p = 1, –5 (mod 12) (주) -1 if p= -1,5 (mod 12)

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

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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)…

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Q: Compute 386 mod 89.

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Q: I have a message 2,3,6,5 (mod.7),  I will find a check digit by multiplying the first and third…

A: Here, First number= 2 Second number =3 Third number= 6 Fourth number= 5

Q: 999 3. Calculate (4) mod 3.

A: This simple result follows by noting that 4 is 1 mod 3. The rest of the details are given in the…

Q: Determine all positive number replacements​ (less than the​ modulus) for the question mark that make…

A: Let the required number be x , where x<1 .

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)…

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Q: (715) (mod 8) (mod 8)

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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: Compute the following: (your answer should be the least nonnegative solution). Show reasoning (i) 87…

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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: 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: If mx = 1 (mod n) has a solution, then nx= 1 (mod m) has a solution. Select one: O True 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: