'Extended gcd algorithm' presentation slideshows

L14: Inverses and GCDs

L14: Inverses and GCDs. Objective: When does have an inverse? How to compute the inverse? Need: Greatest common dividers (GCDs) Results will be used in L15. Reading Textbook, pp. 105-120. Inverses and GCDs. Greatest Common Divisors (GCDs) Definitions

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Chapter 3 Introduction to Number Theory and Its applications

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3 Gallon Jug

Greatest Common Divisor. 3 Gallon Jug. 5 Gallon Jug. Dec 28. This Lecture. Quotient remainder theorem Greatest common divisor & Euclidean algorithm Linear combination and GCD, extended Euclidean algorithm Prime factorization and other applications. The Quotient-Remainder Theorem.

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3 Gallon Jug

Greatest Common Divisor. 3 Gallon Jug. 5 Gallon Jug. Lecture 8: Sep 30. Common Divisors. c is a common divisor of a and b means c|a and c|b . gcd(a,b) ::= the greatest common divisor of a and b. Say a=8, b=10, then 1,2 are common divisors, and gcd(8,10)=2.

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Review for Midterm 1

Review for Midterm 1. Part I: Counting L01-L03 Part II: Number Theory and Cryptography L04, L05. Why counting?. Counting. Principles Sum principle, Product Principle, Bijection Principle Objects to count Lists, functions, subsets, permutations, partitions. Counting Overview.

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3 Gallon Jug

Greatest Common Divisor. 3 Gallon Jug. 5 Gallon Jug. Lecture 8: Sep 29. This Lecture. In this lecture we will learn the Euclidean algorithm for computing greatest common divisor (GCD), which is one of the earliest important

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Modular Arithmetic

Modular Arithmetic. Lecture 8. Modular Arithmetic. Def : a ? b (mod n) iff n|( a - b) iff a mod n = b mod n. Modular Addition. Lemma : If a ? c (mod n), and b ? d (mod n) then a+b ? c+d (mod n). Modular Multiplication.

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