Euler's Theorem
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This document discusses Euler's theorem and Euler's totient function. Euler's theorem states that for any numbers a and n that are relatively prime, a^F(n) is congruent to 1 modulo n, where F(n) is Euler's totient function. The totient function returns the number of positive integers less than n that are relatively prime to n. The document then lists four properties of the totient function and provides examples to illustrate how it can be used to find the totient of various numbers. It concludes by listing numbers to test the reader's understanding of applying the totient function.
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![Cryptography and Network Security
Jeevanantham Arumugam
Euler’s Theorem
For every a and n that are relatively prime then
aF(n)
@ 1 (mod n)
where F(n) is Euler’s Totient Function
F(n) – Number of Positive integers less than ‘n’ and relatively prime to ‘n’
Properties of Euler’s Totient Function:
1. F(1)=1
2. F(P)=P-1 [Condition : P = Prime Number]
3. F(n)= F(PQ) = F(P) * F(Q) = Rule No 2 [Condition : P¹Q & P and Q are Prime
Numbers]
4. F(n) = F(Pi
) = Pi
-Pi-1
[Condition : P and Q are Equal and P is the Prime Number]
Example :
1. F(7) = 6 [Rule 2]
2. F(35) = F(7) * F(5) = 24 [Rule 3]
3. F(49) = F(7) * F(7) = 72
– 72-1
= 42 [Rule 4]
4. F(100) = F(52
) * F(22
) = 40
Test Your Understanding :
• F(41)
• F(32)
• F(35)
• F(600)
• F(140)
• F(625)
• F(35)](https://image.slidesharecdn.com/euler-200805041543/85/Euler-s-Theorem-1-320.jpg)
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Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
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हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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- 1. Cryptography and Network Security Jeevanantham Arumugam Euler’s Theorem For every a and n that are relatively prime then aF(n) @ 1 (mod n) where F(n) is Euler’s Totient Function F(n) – Number of Positive integers less than ‘n’ and relatively prime to ‘n’ Properties of Euler’s Totient Function: 1. F(1)=1 2. F(P)=P-1 [Condition : P = Prime Number] 3. F(n)= F(PQ) = F(P) * F(Q) = Rule No 2 [Condition : P¹Q & P and Q are Prime Numbers] 4. F(n) = F(Pi ) = Pi -Pi-1 [Condition : P and Q are Equal and P is the Prime Number] Example : 1. F(7) = 6 [Rule 2] 2. F(35) = F(7) * F(5) = 24 [Rule 3] 3. F(49) = F(7) * F(7) = 72 – 72-1 = 42 [Rule 4] 4. F(100) = F(52 ) * F(22 ) = 40 Test Your Understanding : • F(41) • F(32) • F(35) • F(600) • F(140) • F(625) • F(35)