a) Show that 2340 1 (mod 11) by Fermat's little theorem and noting that 2340 =
Question:
b) Show that 2340 ≡ 1 (mod 31) using the fact that 2340 = (25)68 = 3268.
c) Conclude from parts (a) and (b) that 2340 ≡ 1 (mod 341).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 71% (7 reviews)
a We calculate 2 340 2 10 34 1 34 1 mod 11 since Fermats li...View the full answer
Answered By
Jonas Araujo
I have recently received the degree of PhD. In Physics by the Universidade Federal do Maranhão after spending a term in Durham University, as I have been awarded a scholarship from a Brazilian mobility program. During my PhD. I have performed research mainly in Theoretical Physics and published works in distinguished Journals (check my ORCID: https://orcid.org/0000-0002-4324-1184).
During my BSc. I have been awarded a scholarship to study for a year in the University of Evansville, where I have worked in detection-analysis of photon correlations in the the Photonics Laboratory. There I was a tutor in Electromagnetism, Classical Mechanics and Calculus for most of that year (2012).
I am very dedicated, honest and a fast learner, but most of all, I value a job well done.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Discrete Mathematics and Its Applications
ISBN: 978-0073383095
7th edition
Authors: Kenneth H. Rosen
Question Posted:
Students also viewed these Statistics questions
-
This exercise outlines a proof of Fermat's little theorem. a) Suppose that a is not divisible by the prime p. Show that no two of the integers 1 a, 2 a, . . . , (p 1)a are congruent modulo p. b)...
-
Show that if n | m, where n and m are integers greater than 1, and if a b (mod m), where a and b are integers, then a b (mod n)?
-
Show that if a, b, k, and m are integers such that k 1, m 2, and a b (mod m), then ak bk(mod m)?
-
In Exercises find the second derivative of the function. f(x) = x + 3x-3
-
Draw a level 0 data flow diagram (DFD) for the university system in Exercise D, Chapter 4.
-
What are the three characteristics of a liability and why does a deferred tax liability of a corporation meet these characteristics?
-
Phone Screens and Computer Screens are two divisions operated as investment centres of Malta Ltd. Management wants to know which of the two earned the highest return on investment for the year ended...
-
A quant jock from your firm used a linear demand specification to estimate the demand for its product and sent you a hard copy of the results. Unfortunately, some entries are missing because the...
-
You are provided with the following information for Carla Vista Co., effective as of its April 30, 2025, year-end. Accounts payable $844 Accounts receivable 840 Accumulated depreciation-equipment 640...
-
Consider motionless air with p 1 = 0.1 atm and T 1 , = 300 K in a constantarea tube. We wish to accelerate this gas to Mach 1.5 by sending a normal shock wave through the tube. Calculate the...
-
Use Fermat's little theorem to show that if p is prime and p X | a, then ap2 is an inverse of a modulo p.
-
Show that if p is an odd prime, then every divisor of the Mersenne number 2p 1 is of the form 2kp + 1, where k is a nonnegative integer.
-
What are the components of total acquired cost? Is it realistic to expect companies to consider all of these components?
-
Explain carefully why a bank might choose to discount cash flows on a currency swap at a rate slightly different from LIBOR.
-
Identify the sources of marine pollution and the manner in which UNCLOS regulates them.
-
In your view, is the regulation of land-source marine pollution adequate?
-
Why might severe fiscal imbalances lead to financial crises in emerging market economies?
-
MARPOL, along with its Annexes, is sufficiently detailed and comprehensive to achieve its objective of eliminating marine pollution arising from harmful substances, and the fact it has not achieved...
-
Write Verilog code for the FSM described in Problem 6.3. Data From Problem 6.3. Derive the state diagram for an FSM that has an input w and an output z. The machine has to generate z = 1 when the...
-
Tanaka Company's cost and production data for two recent months included the following: March April Production (units).........300................600 Rent.....................$1,800............$1,800...
-
Samples of a Fast aluminum part are classified on the basis of surface finish (in micro inches) and edge finish. The results of 100 parts are summarized as follows: Edge finish Excellent Good Surface...
-
Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows: Conforms Yes No 1 22 8 Supplier 2 25 5...
-
Use the axioms of probability to show the following: (a) For any event. E, P (E) = 1 P (E). (b) P () = 0 (c) If A is contained in B, then P (A) < P (B)
-
The following table shows the data from 2000 general social survey. The table cross classifies gender and political party identifications. Subjects indicated whether they identified more strongly...
-
The Information Richness of Communication Media The four types of communication media are Face-to-face Communication, Spoken Communication Electronically Transmitted, Personally Addressed Written...
-
Once you've chosen your company or product, explain why you would not purchase from that company or that product. Be sure to give an argument making use of moral principles to support your statements.
Study smarter with the SolutionInn App