# w7 - Math 55 Worksheet Adapted from worksheets by Rob...

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

Math 55 Worksheet Adapted from worksheets by Rob Bayer, Summer 2009. Warmup 1. Solve the congruence 5 x 16( mod 21) Linear Congruences and the CRT 1. Solve the system of congruences x 3 ( mod 4) x 2 ( mod 5) x 5 ( mod 7) 2. Solve the system of congruences 2 x 1 ( mod 3) 3 x 2 ( mod 5) 4 x 1 ( mod 7) 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). 4. Compute the following: (a) 7 130 mod 11, (b) 4 16 mod 10, and (c) 10 4 16 mod 11. 5. F Let p be a prime number and let A = { 1 , 2 , ··· ,p - 1 } . Because all elements of A are relatively prime to p , they all have inverses (mod p ). Let

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.

## This note was uploaded on 02/06/2012 for the course MATHEMATIC 55 taught by Professor Robbayer during the Summer '09 term at University of California, Berkeley.

### Page1 / 2

w7 - Math 55 Worksheet Adapted from worksheets by Rob...

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

View Full Document
Ask a homework question - tutors are online