3. Find an inverse, if exists, of 12 mod 15.

Q: If a mod b = 0, then b | a O True O False

A:

Q: Find an integer x satisfying the equation: 4x21 = 2(mod 5) or show that no such integer exists.

A:

Q: Find the solution to 34x = 77(mod 89) that is positive and less than 89.

A: given that                                          34x≡77 (mod 89) we have to find positive…

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

A: Given b is an integer such that b mod12=5 To find the value of  6b mod12

Q: Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12…

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

Q: Find the inverse of 42 (mod 8) or state why it cannot exist. Find the inverse of 17 (mod 5) or state…

A: Given: a) Find the inverse of 42(mod 8) or state why it cannot exist. b) Find the inverse of 17(mod…

Q: Find 12 ^– 1(mod 17), the inverse of 12 modulo 17

A: Find an inverse of 12 modulo 17 as follows.

Q: (c) For each integer a, if a 4 (mod 8), then a 2 (mod 8).

A:

Q: Find the value of 3443 mod 23 4 16 O 3

A:

Q: Compute 2021^2021(mod 1000). The answer is 421. Show the work.

A:

Q: The inverse of 7 modulo 26 is 15

A: Given a statement

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

A:

Q: In mod n arithmetic why does x have a multiplicative inverse if and only if x is relatively prime to…

A:

Q: Al. b. Find the inverse of 17 modulo 23, if exists. If not, give reasons.

A: The objective is find the inverse of 17 modulo 23 if exists or else give the reason why it does not…

Q: 5x = 7 (mod 32)

A: To solve the following problem

Q: Let a, n be positive integers. Knowing that 15a - 13n = 1, we deduce that the multiplicative inverse…

A:

Q: Calculate the inverse of 15 mod 26 (i.e., solve 15 * x ≡ 1  (mod 26))

A:

Q: (d) Using the result in (c) find the inverse of 45 mod 17.

A: (d) we see that, 17×8 + 45×(-3) = 1, Where, p = 8 and q = -3

Q: d) If 72 = 1 (mod 5), with 0<r <4, then z =. e) The number of (positive) divisors of 23345 is

A:

Q: Q1 Prove or disprove i. If ac = bc(mod m), then a = b(mod m).

A:

Q: Find a number a such that 70a = 1 mod 17.

A:

Q: The last two digits of 52044 is 44. If ab = 0 (mod 3), then a = 0 (mod 3) or b = 0 (mod 3). F 10. F…

A:

Q: Write the set of solutions of x=5 (mod 24) x= 17 (mod 18), if any as the solutions to a single…

A: We have a set of congruence as x ≡ 5 (mod 24)x ≡ 17 (mod 18) From the first equation we can write…

Q: Find the inverse of 47 mod 30 or 47 x = 1 (mod 30)

A:

Q: Find the inverse of 9 (mod 10).

A: Just I have used the note about inverse of a modular and find that  Inverse of 9(mod10) is 9

Q: Prove that for any integer x, if x mod 3 does not divide 0, then (x2 −3x + 1) mod 3 = 2.

A:

Q: a) What does it mean for a to be an inverse of a modulo m? b) How can you find an inverse of a…

A:

Q: The order of 2 mod 17 is: a) 2 b) 4 c) 8

A: The order of a modulo p then is the least positive integer n such that an ≡ 1(mod p) where p is a…

Q: Suppose that a and b are integers, a = 4(mod 13), and b = 9(mod 13). Find the integer c with 0<c< 12…

A: We will use the basic properties of congruence modulo n relation to answer this question.

Q: Find all inverses of 7 modulo 37.

A:

Q: Find the multiplicative inverse of 8 mod 11

A: SOLUTION-

Q: Suppose b is any integer. If b mod 12 = 7, what is 5b mod 12? In other words, if division of b by 12…

A:

Q: use the Euclid's algorthim to find the inverse for 76 mod 83

A:

Q: Suppose that a and b are integers, a = 4 (mod 13), and b = 9 (mod 13). Find the integer c with 0 < c…

A:

Q: The multiplicative inverse of 103 (mod 120) * O is 7(mod 120) O None of these is 50(mod 120) is…

A:

Q: Suppose b is any integer. If b mod 12 = 7, what is 6b mod 12? In other words, if division of b by 12…

A: To determine the value of 6b mod(12) if b mod(12) = 7.

Q: False In mod 7 arithmetic,

A: Introduction: Modular arithmetic is an integer-based arithmetic method that takes the remainder into…

Q: find the inverse. of 47 mod 30 or 47 x = 1 (mod 30) using Euclidean Algori thm).

A: Congruences

Q: Which of the following sets is dlosed under the given operation? O {1, 4, 5, 7} multiplication mod 9…

A: Group. Solving ques 1 According to guidelines.

Q: Prove that for each integer a, if a not equal to 0 (mod 7), then a2 not equal to 0 (mod 7)

A: Consider the provided question,

Q: 3. If x mod 4 = 1 and y mod 4 = 3, then xy could be O 901 O 299 O 508 O 113

A: We shall use the division algorithm

Q: 501 a. Find 200 mod 17 b. Find inverse of 7 mod 31.

A: To find a) 2501 mod 17. b) The inverse of 7 mod 31.

Q: 5. If a-l is the inverse of a modulo m and b-1 the inverse of b modulo m, show that a--1 is the…

A:

Q: According

A: We know that,  If a, p are integers and p is any prime such that gcd(a,p)=1 then ap-1=1 mod p.

Q: Which of the following sets is closed under the given operation? O {1, 4, 13} multiplication mod 15…

A: {0,4,8,16} addition mod 16 And 2/x

Q: If 3(26!) = x(mod29), then x = None of the choices O 11 13 15

A: The given problem is to solve the given congruence equation. 3(26!)= x (mod 29).