Question: Prove that if a and b are any positive integers such that a | b, then (x mod b) mod a = x mod a

Prove that if a and b are any positive integers such that a | b, then (x mod b) mod a = x mod a for any x. Prove, under the same assumptions, that x = y (mod b) implies x = y (mod a) for any integers x and y.

Step by Step Solution

★★★★★

3.27 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Given that a and b are any positive integers such that a b we must show that x mod b mod a x mod a for any x Recall that x mod a is the remainder of x ... View full answer

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 Introduction to Algorithms Questions!

Prove that if A and B are skew-symmetric n n matrices, then so is A + B.

Prove that if A and B are n n matrices, then tr (AB) = tr (BA).

Prove that if A and B are n n matrices, then (a) tr(KA) = k tr(A) + tr(B) (b) tr(AB) = tr(BA)

ALGEBRAIC For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. 3. log. (7x . 2y) 5. log.( 17 ) 7. In (4) For the...

Prove that log b (n) =1/log n (b) for any positive integers b > 1 and n > 1.

Proof 1: Logical Reasoning and Proofs: Application Server Load Assume you have been tasked with assessing the "load" or "user traffic" that users might impose on your company's servers. Specifically,...

In cryptography, it is important to be able to find bn mod m efficiently, where b, n, and m are large integers. It is impractical to first compute bn and then find its remainder when divided by m...

644 Click and drag the given steps to their corresponding step names to find 11 4 mod 645 using the given algorithm procedure modular exponentiation( b: integer, n = (ak-lak-2-a,ao)2, m: positive...

2. Let f(x,y) be a positive definite quadratic form. Then Conway's topograph has either a simple well or a double well. Suppose that Conway's topograph has a simple well. Let a,b,c be the values of...

[44] Show that simulating a linear-time 2-tape deterministic Turing machine with one-way input by a 1-tape nondeterministic Turing machine with one-way input requires (n2/((log n)2 log log n)) time....

In the book How to Win Friends and Influence People, explain the key factors and why your selection highlights your opinion about entrepreneurship.

I. Using vertical analysis (show your calculations), present the following values for this year and last year: a) gross profit margin b) net profit margin (use the last "net income" line on the...

8. LO.3, 4 Lori wants to establish that her niece Suzette actually qualifies for a dependency exemption. After the issue is raised by the IRS on audit, Lori could argue the matter with the agent, an...

What laws were probably being violated?

In a nonpersistent HTTP connection, how can HTTP inform the TCP protocol that the end of the message has been reached?

In HTTP, draw a figure to show the application of cookies in a scenario in which the server uses cookies for advertisement. Use only three sites.

When an HTTP server receives a request message from an HTTP client, how does the server know when all headers have arrived and the body of the message is to follow?

A store has 5 years remaining on its lease in a mall. Rent is $1,900 per month, 60 payments remain, and the next payment is due in 1 month. The mall's owner plans to sell the property in a year and...

17. Asset allocation is the: A. selection of specific securities within a particular class or industry. B. decision on which exchange to sell or buy an asset. C. division of a portfolio into long and...