s7 - Math 55 Worksheet Adapted from worksheets by Rob Bayer...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Math 55 Worksheet Adapted from worksheets by Rob Bayer, Summer 2009. Warmup 1. Solve the congruence 5 x 16( mod 21) x =- 4 Linear Congruences and the CRT 1. Solve the system of congruences x 3 ( mod 4) x 2 ( mod 5) x 5 ( mod 7) Solution: x 47 mod 140. 2. Solve the system of congruences 2 x 1 ( mod 3) 3 x 2 ( mod 5) 4 x 1 ( mod 7) Solution: To start this one, notice what happens if we multiply both sides of the first equation by 2! Since 2 2 1 mod 3, the first equation is the same as x 2 mod 3. Similarly, we take care of the other equations. Heres a website which talks about the CRT and has a calculator to help you solve problems like this: (And plenty of other good resources too! http://www.math.mtu.edu/mathlab/COURSES/holt/dnt/chinese3.html) 3. F Suppose we want to find all solutions to x 2 4 ( mod 35) (a) Show that such solution must also be a solution to the system ( x 2 4 ( mod 5) x 2 4 ( mod 7) and vice-versa. (b) Show that, based on the conditions in (a), x 2 or 3 ( mod 5) and that x 2 or 5 ( mod 7). (c) Use the CRT on each of the possibilities from (b) to find all solutions to x 2 4 ( mod 35)....
View Full Document

Page1 / 2

s7 - Math 55 Worksheet Adapted from worksheets by Rob Bayer...

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

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