Question: Prove that the linear congruence ax?1(mod n) has a solution for x if and only if (a,n)=1.

Prove that the linear congruence ax?1(mod n) has a solution for x if and only if (a,n)=1.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Prove the following using the above theorem. Let m,.., nk be positive integers (NOT necessarily relatively prime) and x ::.til. m()d (n.).. " ", x: :ak n )(l (FAM.) a solution if and only if gcd(ni,...

Q:

1. (a) We will say that two positive integers, ni and nj, are relatively prime if the greatest common divisor of n, and nj is 1. Suppose that we are given a system of equations: x = a mod n x = a2...

Q:

Consider the following problem: - Input: n : positive integer - Output: number of quadratic nonresidues modulo n, where a quadratic nonresidue mod n is an integer r in the range of 0 to n - 1 such...

Q:

Please solve computer project on mathCAD, please post pictures of code. Will give instant thumbs up! Instructions: Follow the directions given below to create a MathCAD worksheet for implementing the...

Q:

Using the last statement in Theorem 46.9, show that for nonzero a, b, n Z, the congruence ax b (mod n) has a solution in Z if a and n are relatively prime. Data from Theorem 46.9 Let D be a...

Q:

Prove that the equation ax ay (mod n) implies x y (mod n) whenever gcd (a, n) = 1. Show that the condition gcd (a, n) = 1 is necessary by supplying a counterexample with gcd (a, n) > 1.

Q:

Find the particular solution of the following system of linear difference equations with given initial value conditions (n)=-2(n-1)+2y(n-1); x (0) = =-2 y (n) = x (n 1) + 2 y (n 1); y (0) = 3...

Q:

MATH 135 S 2016: Assignment 9 Solutions 1. Prove that for any integer n, 441n43 + 374n35 + 285n23 0 (mod 55). Solution: Since 55 = 5 11 and gcd(5, 11) = 1, we may use the Splitting Modulus...

Q:

1. Find an inverse of a modulo m for each of these pairs of relatively prime integers using the method followed in example below. a.) a = 4 , m = 9 b) a =19, m = 141 c) a = 55, m = 89 d) a = 89, m =...

Q:

pleaseanswerthese (1 point) Encrypt the message " HALT " by translating the letters into numbers (via A = 0, B = 1, C = 2, D = 3, E = 4, F = 5, G = 6, H = 7, 1 = 8, J = 9, K = 10, L = 11, M = 12, N =...

Q:

A building acquired at the beginning of the year at a cost of $92,600 has an estimated residual value of $3,600 and an estimated useful life of 10 years. Determine the following: (a) The depreciable...

Q:

Which of the following metals is not found in the free state in nature: Ag, Cu, Zn, Au, Pt?

Q:

Seved Help Save & Exit Which of the following is not a term that describes part of the accounting for noncurrent assets? Multiple Choice Depreciation Accumulation Amortizatit Depletion odwill is an...

Q:

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.