This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 3 S 3 )%m 3 =(6 S 3 )%7=1 Thus, (S 1 , S 2 , S 3 ) = (1,2,6) For a residual number (0,2,1): x=(M 1 S 1 r 1 + M 2 S 2 r 2 + M 3 S 3 r 3 )%M 5 Example For a residual number (1,2,5): x=(M 1 S 1 r 1 + M 2 S 2 r 2 + M 3 S 3 r 3 )%M = (2111 + 1422 + 665)%42 = (21 + 56 + 180)%42 = 257%42 = 5 6 Proof of Chinese Remainder Theorem Let A = i=1,k (M i S i r i ), we show that 1. A%m v = r v and 2. x=A%M is unique. 1. A%m v = ( i=1,k (M i S i r i ) )% m v = ((M i S i r i ) % m v )%m v = (M v S v r v )%m v = [(M v S v )%m v r v %m v ]%m v = r v %m v = r v 2. Proof was shown in lecture 5. 7...
View
Full
Document
This note was uploaded on 12/11/2011 for the course CSE 20 taught by Professor Foster during the Fall '08 term at UCSD.
 Fall '08
 Foster

Click to edit the document details