A. Show that if gcd(a, 65) = 1 then a 1 (mod 55). В. Use the binary exponentiation algorithm to compute 14155 (mod 1537).

Q: Establish by mathematical induction that any postage of at least 12c can be obtained using 3c and 7c…

A: We have to establish by mathematical induction that any postage of at least 12c can be obtainedusing…

Q: 6. (a) Find the least positive inverse for 23 modulo 216 using Extended GCD algorithm only. (b)…

A: (a) Find the least positive inverse for 23 modulo 216 using Extended GCD algorithm. (b) Prove that…

Q: Use Eulers thm to find , 7଼8003 mod 1000

A:

Q: 2r = 3 4x = 2 3x 2 (mod 5) (mod 6) (mod 7).

A:

Q: Books are identified by an International Standard Book Number (ISBN), a 10-digit code x1x2... x10,…

A: Let us start finding q and m values

Q: Determine the least residue of 56^1010 (mod 323).

A:

Q: Find 8081 mod 11.

A:

Q: 11. Prove that a¹ = 1 (mod 5) for every integer a that is not divisible by 5.

A: We have to prove  for every integer  that is not divisible by

Q: Use the EXTENDED EUCLIDEAN ALGORITHM to compute the following mul- tiplicative inverses: (a) 17-¹…

A: The extended Euclidean algorithm is an algorithm to compute the integers x and y such that for given…

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

A:

Q: Find the inverse of 35 under mod 233(if exixts), by using Euclid's Algorithm?

A:

Q: x² + 4x = 10(mod11) (mod11) X=

A: Given that x2+4x≡10 (mod 11)x2+4x+4≡10+4 (mod 11)x2+4x+4≡14 (mod 11)x2+4x)(x+2)2≡14+11 (mod…

Q: (d) Find an integer x, 0 < < 18, that satisfies the following congruence: 9x + 13 = 10 (mod 19).…

A: (d) Given is a congruence 9x+13≡10(mod 19)   To Find: An integer x such that 0≤x≤18 that satisfies…

Q: Suppose that the most common letter and the second most common letter in a long ciphertext produced…

A:

Q: B- What is the multiplicative inverse of x¹5 in Z₂[x] (mod x² + x + 1)?

A:

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

A:

Q: Q-2: a) Four married couples have bought 8 seats in the same row for a concert. In how many…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find all integers sx such that 2x = 5 (mod 7).

A:

Q: Let a, b and c a=1b=0C=9 example with enrolment number 001054321, you would take a = 0, b = 5 and c…

A: The answer to the given question is provided below with respective explanation.

Q: O Find 5675 (mod 19

A:

Q: 1. Compute without a calculator: (a) 59 + 63 mod 13 (b) 15 * 29 mod 13 (c) 2 * 29 mod 13 (d) –10 *…

A: Since there are multiple questions the first question and the first three subparts is answered.…

Q: Compute 25200 mod 27.

A: As 25 is coprime to 27, by Euler's theorem, we see        25φ(27) ≡ 1 (mod 27)  Now,        φ(27) =…

Q: Use the binary exponentiation algorithm to compute 41 (mod 409)

A:

Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

A: We have to solve the equation 1 = 3x + 2 (mod 7)⇒1 - 2 - 3x = 0 (mod 7)⇒-1 - 3x = 0 (mod 7)⇒3x = - 1…