Question: Let a, b, m, n Z with m, n > 0. Prove that if a = b (mod n) and m , then a

Let a, b, m, n ∈ Z with m, n > 0. Prove that if a = b (mod n) and m\n, then a = b (mod m).

Step by Step Solution

★★★★★

3.49 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Proof Since a b mod n we m... View full answer

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

Document Format (1 attachment)

Word file Icon

954-M-L-A-L-S (8428).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(a) How many paths of length 4 are there in the complete graph K7? (Remember that a path such as v1 v2 v3 v4 v5 is considered to be the same as the path v5 v4 v3 v2 v1.) (b) Let m, n Z+ with...

Q:

a. Let A = {1, 2, 3, 4, 5, 6, 7} and B = {v, w, x, y, z}. Determine the number of functions /: A B where (i) f(A) = {v, x}; (ii) |f(A)| = 2; (iii) f(A) = {w, x, y}; (iv) If(A) | = 3; (v) f(A) = {u,...

Q:

Let m, n Z+ with m n. Under what condition(s) on m, n will every edge in Km,n be in exactly one of two isomorphic subgraphs of Km,n?

Q:

X Course Hero Differential Equations and Linear X G Determine all values of the const x M (no subject) - sylviaabdelmasih@ x...

Q:

it network: Digital logic graph Styles Question [1]: [25 marks] A combinational circuit is divided into two sub-circuits N1 and N2 as shown. The truth table for N1 is given. Assume that the input...

Q:

Instructions The following five sections; Direct proof Proof by contrapositive Proof by contradiction Proof with cases Proof of a biconditional Two proofs in each section from the proposed exercises....

Q:

Developments in Technology Light is incident from air on the end face of a multimode optical fibre at angle of incidence as shown below. n n 1 2 The refractive indices of the core and cladding are...

Q:

Department of Computer Science & Software Engineering Comp232 Mathematics for Computer Science Winter 2017 Assignment 3. Due date: March 30, by 23:59 EDT 1. For each of the following, determine...

Q:

39. Let G = {3"6" I m, n E Z) under multiplication. Prove that G is isomor- phic to Z Z. Does your proof remain valid if G = {39" \\ m, n E Z}? 40. Let (a , a,, . . ., a) EG OG, O . . . OG . Give a...

Q:

can you help with this proofs (algebra) question. Can you help with this question (question 9 or Q9) [3 marks) and express all of them in exponential form. form. (2) Find the product of the three...

Q:

Equipment acquired on October 4, 2022 at a cost of $540,000 has an estimated useful life of 10 years. The residual value is estimated to be $54,000 at the end of the equipment's useful life. The...

Q:

In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained. Use a 0.05 significance level to test the claim that getting a cold is...

Q:

3 Taupe, a calendar year taxpayer, has the following capital transactions for 2017: long-term capital loss of $4,000 and a short-term capital loss of $4,000. How are these items handled for tax...

Q:

Dorinda, Luis, and Elizabeth form a limited partnership. Dorinda is a general partner, and Luis and Elizabeth are limited partners. Consider each of the separate events below, and discuss fully which...

Q:

This 26-by-21 cm rectangle has been divided into two regions. The width of the unshaded region is x cm, as shown. a. Express the area of the shaded part as a function of x, and graph it. b. Find the...

Q:

Consider the polynomial equation 0 = 3x4 - 20x3 + 68x2 - 92x - 39. a. List all possible rational roots. b. Find the four roots of the equation.

Q:

Write each expression in the form a + bi. a. (4 - 2i) (-3 + 6i) b. (-3 + 4i) - (3 + 13i) c. 2 - i / 3 - 4i

Q:

Please solve parts c and d. DO NOT reuse a former solution. For part 2c, make sure to show all work to show if it is CONSISTENT or not. Show the work for variance, expected value, and limits. For d,...

Q:

Fishing supply company, Outside Tackle, has its returns graphed against the market returns for a 5 year period. The line that has the best fit for the data has the formula y = .1254 + 1.265x. What...

Q:

I need to know the math behind these answers. 7. (12 points) Suppose you have sold short 900 shares of Fallcorp stock at $80 per share. You have posted the 60% margin required on the short sale. The...