Lecture_19 - MA1100 Lecture 19 Functions/Number Theory...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
1 MA1100 Lecture 19 Functions/Number Theory Inverse functions Greatest Common Divisor Euclidean Algorithm
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA1100 Lecture 19 2 Common divisor Recall 1 Recall 2 Let a, b be integers and d a nonzero integer. Let n be an integer and m a non-zero integer. We say m divides n and write m | n if there exists an integer q such that n = mq . We also say m is a divisor of n. We say d is a common divisor (factor) of a and b if d | a and d | b .
Background image of page 2
MA1100 Lecture 19 3 Common divisor Example Let a = 48 and b = 84. Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Divisors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Common divisors of 48 and 84: 1, 2, 3, 4, 6, 12 The greatest common divisor of 48 and 84 is 12 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MA1100 Lecture 19 4 Greatest common divisor Definition Notation The largest integer that divides both a and b is called the greatest common divisor of a and b. gcd(a, b) Let a, b be integers, not both 0. Example gcd(48, 84) = 12 Remark gcd(0, 0) = ?
Background image of page 4
Lecture 19 5 Basic properties of GCD 1.gcd(a, b) > 0 2.gcd(a, a) = |a| 3.gcd(a, 0) = |a| 4.gcd(a, b) = gcd(-a, b) = gcd(a, -b) = gcd(-a, -b) gcd(48, 48) = 48 gcd(-48, -48) = 48 gcd(48, 0) = 48 gcd(-48, 0) = 48 whether a and b are positive or negative Let a and b be integers with a 0. gcd(48, 84) = gcd(-48, 84)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/19/2012 for the course SCIENCE MA1100 taught by Professor Forgot during the Fall '08 term at National University of Singapore.

Page1 / 22

Lecture_19 - MA1100 Lecture 19 Functions/Number Theory...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online