Use the modular inverses found in the preceding problem to solve the following congruences, if possible, by multiplying by the inverse 1. 80r = 51 (mod 171) 2. 200z = 73 (mod 171) 3. 15x = r (mod 79)

Q: From the following list of integers 2 7 9 11 12 13, which integer is the multiplicative inverse of…

A:

Q: 2. Solve the following polynomial congruences. ces (a) x² + 12x – 17 = 0 (mod 143) (b) x³ + 30x² +…

A:

Q: 4444 is divided by a 1.19) find the remainder when 4444 * 2?=-1 (mod a).

A: 1.19 We have 4444  ≡  7 (mod 9). So, 44444444 ≡ 7 4444 (mod 9) Now,       73 ≡1 (mod 9) Or,…

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: Solve each of the following congruences. (a) 6x + 3 = 4 mod 10 (b) 6x + 3 = 1 mod 10 (c) x² = 1 mod…

A: In congurent modulo n, ax≡bmod n has exactly 'd' solutions if 'd' divide 'b'where d=gcda,n otherwise…

Q: As a small illustration of Chinese remainder theorem that can all be solved mentally, say M = 30.…

A: The Chinese Remainder Theorem:                               Let m1,m2,.......mk be a collection of…

Q: Solve the following quadratic equation via the two different methods namely both classical and…

A: The equation a≡b mod n means that a-b is divisible by n. That is, the remainder when a-b is divided…

Q: Solve the congruency by finding the inverse: 7x = 9(mod 43)

A:

Q: Modular division can be performed by considering the related multiplication problem. For instance,…

A:

Q: Find d the inverse of 43 mod 6602

A: we use Euclidean algorithm to find the inverse of 43 mod 660.

Q: y = 3x - 5 mod 26 СРHТXT

A: Let us consider the equation y≡ax+b(mod 26) To decrypt the message  Convert the equation in terms…

Q: (c) Find integers p and q so that 17p + 45q = 1. Show your working steps. (d) Using the result in…

A: Given that 17p+45q=1 has no solution such that p and q are integers which means gcd of (17, 45) is 1…

Q: If x is positive, the first negative term in the expansion of (1 + x)27/5 is (a) 5th term (b) 6th…

A: Introduction :

Q: a. Find an inverse for 210 modulo 13. b. Find appositive inverse for 210 modulo 13. c. Find a…

A: a) To find an inverse for 210 modulo 13. b) To find a positive inverse for 210 modulo 13. c) To find…

Q: Find an inverse modulo 13 of each of the following integers. a) 2 b) 3 c) 5 d) 11

A: if a number n has x (integer) as its inverse modulo 13 then n·x ≡ 1(mod 13) ⇒ n·x = 13k+1 here k is…

Q: (4) Apply the Fast Modular Exponentiation to find 0 < M < 87, where 5015 = M mod 87.

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

A:

Q: One of the following is a solution of 306x = 90 (mod 360) 107 has no solution 105 106 108

A:

Q: can be used as a serial to parallel converter Decoder De--Multiplexer Encoder Multiplexer The…

A: We have to choose the correct option.

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: Solve for x using The Division Algorithim : 937 =x (mod 4)

A:

Q: 3. First solve for q: (a) 143 = 1( mod 2) (b) Rewrite 143 as the product of 11 x 13 and show that…

A: Consider the given information: a=q m+ r Where a= dividend , q=quotient, m=mod , and r=remainder. To…

Q: Decide whether the following binomial congruence has any solutions x2" = 10 mod 103. Use modular…

A: We have to decide whether the following binomial congruence has any solutions or not.…

Q: Is -3 a multiplicative inverse of 17 mod 26? Show all workings.

A:

Q: (b) Find the remainder of (10100) (10+00) mod 13.

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: Find s e Z with 0ss< 13, so that s = 127+300(mod 13). Your work should show a method that does not…

A:

Q: Rewrite 17x=3 (mod 53) as linear combination. b) Using Euclidean Algorithm to find the gcd(17, 53).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Determine whether e(x)=15x+4(mod 26) and e(x)= 4x+5(mod 26) are invertibles or not. If yes, find the…

A: We are asked to determine if the given equation are invertible and if they are we have to find the…

Q: Find the multiplicative inverse of 8 mod 11

A: SOLUTION-

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

A:

Q: Then Find inverse of 21 mod 200.

A:

Q: a. Find the inverse of 43 (mod 256) b. Solve the linear congruence 43x=7(mod 256)

A:

Q: Answer the following. 1. Find x if 2x309 is divisible by 9 2 Find the canonical prime factorization…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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

A: Congruences

Q: Q7 Compute 59^11 mod 13 Note: You should be able to do this using the modulo squaring method and…

A: 59^11 mod13

Q: ere they want me to find a div m and a mod m when a = −33, m = 67. How I solved, I divided -33 into…

A: To find a div m and a mod m when a = −33, m = 67. Given information:  a = -33 m = 67

Q: Show 3^1728 ≅ 1mod19 Please do this using the method where you start with 3 to smaller powers and…

A:

Q: Use the {\bf Cayley Hamilton Theorem} to come up with an expression for A" in terms of n when 1 A =

A: As you have asked more than one question, we shall answer first Que only. For others kindly post…

Q: Compute the following modular inverses. (Remember, this is *not* the same as the real inverse). 1/9…

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: 3) Find 3521 mod 645 by modular exponentiation. You must show your work step by step.

A: Solution: 3521 mod 645

Q: Suppose a # b (mod m). Let r be the remainder of a when divided by , and let s be the remainder of…

A:

Q: Solve (by hand) 6x 5 mod (151) using Pohlig-Hellman. You may use wolfram alpha to do simple…

A: To solve : 6x=5mod151 using Pohlig-Hellman

Q: 1)For each of the following, find an integer value x which satisfies the equation, or explain why…

A:

Q: 10. Solve the following quadratic equation via the two different methods namely both classical and…

A: