We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
supports HTML5 video
Published byEthan Bradshaw
Modified over 5 years ago
mod arithmetic a mod m is the remainder of a divided by m a mod m is the integer r such that a = qm + r and 0 <= r < m again, r is positive Examples 17 mod 3 = 2 17 mod 12 = 5 (5 o’clock) -17 mod 3 = 1
congruences a is congruent to b modulo m if m divides a - b
a is congruent to b mod m if and only if the remainder of adivided by m is equal to the remainder of b divided by m. proof
If a is congruent to b mod m and c is congruent to d mod mthen a+c is congruent to b+d mod m proof
If a is congruent to b mod m and c is congruent to d mod mthen ac is congruent to bd mod m proof
Mod arithmetic examples -133 mod 9 = 2 (but in Claire?) list 5 numbers that are congruent to 4 modulo 12 hash function h(k) = k mod 101 h( ) h( ) h( ) h( )
Division & Divisibility. a divides b if a is not zero there is a m such that a.m = b a is a factor of b b is a multiple of a a|b Division.
Binary Relations Binary Relations on Real Numbers.
MS-Excel XP Lesson 5. Exponentiation 1.A1 2 A2 3 A3 =A1^A2 B1 =2^4 2.^ for exponentiation.
Chapter 4 Finite Fields. Introduction of increasing importance in cryptography –AES, Elliptic Curve, IDEA, Public Key concern operations on “numbers”
Cryptography and Network Security Chapter 4 Fourth Edition by William Stallings.
Chapter 4 – Finite Fields. Introduction will now introduce finite fields of increasing importance in cryptography –AES, Elliptic Curve, IDEA, Public Key.
Prime and Composite Numbers
1 Section 2.4 The Integers and Division. 2 Number Theory Branch of mathematics that includes (among other things): –divisibility –greatest common divisor.
Arithmetic Intro Computer Organization 1 Computer Science Dept Va Tech February 2008 © McQuain Algorithm for Integer Division The natural (by-hand)
Converting Numbers Between Bases. While the quotient is not zero… Divide the decimal number by the new base. Make the remainder the next digit to.
Congruence class arithmetic. Definitions: a ≡ b mod m iff a mod m = b mod m. a [b] iff a ≡ b mod m.
Chapter 4: Elementary Number Theory and Methods of Proof
Cyclic Groups. Definition G is a cyclic group if G = for some a in G.
Number System Conversions Lecture L2.2 Section 2.3.
© 2007 M. Tallman. - - Step 1: Divide (÷) Step 2: Multiply (×) Step 3: Subtract (-) Step 4: Bring Down ( ↓ ) Step 5: Repeat or Remainder ) 43 5 How many.
Patterns and Sequences. Patterns refer to usual types of procedures or rules that can be followed. Patterns are useful to predict what came before or.
Sub Title Factors and Multiples Chapter 3: Conquering SAT Math.
Objective: Learn to multiply and divide integers.
EXAMPLE 1 Same sign, so quotient is positive. = –7 Different signs, so quotient is negative. c. 36 –9 = –4 Different signs, so quotient is negative. =
© 2019 SlidePlayer.com Inc. All rights reserved.