# NT2009HW3 - 4400/6400 PROBLEM SET 2 A sufficient number of...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4400/6400 PROBLEM SET 2 A sufficient number of problems: 6 for 4400 students, 8 for 6400 students. The first four problems pertain to the Euclidean Algorithm, which will be applied to positive integers a b 1. 2.1) Explain how to use a nonprogrammable handheld calculator to find the q and the r such that a = qb + r . 2.2) Use the Euclidean Algorithm to find the gcd of 12345 and 67890. 2.3) Let us analyze the Euclidean algorithm applied to integers a b 1. It is helpful to give a precise labelling to the sequence of remainders: r- 1 = a , r = b , r i- 1 = q i +1 r i + r i +1 . The algorithm terminates as soon as it reaches an n such that r n +1 = 0. a) Explain why we have that for all i ,- 1 i n , 0 r i +1 &lt; r i , and why this im- plies that the algorithm is guaranteed to terminate (i.e., it really is an algorithm). b) Show that r n , the last nonzero remainder, is equal to gcd( a, b )....
View Full Document

## This note was uploaded on 10/26/2011 for the course MATH 4400 taught by Professor Staff during the Spring '11 term at University of Georgia Athens.

### Page1 / 2

NT2009HW3 - 4400/6400 PROBLEM SET 2 A sufficient number of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online