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

A: Image is attached with detailed solution.

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

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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: 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)…

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

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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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