Digital Codes: Practice 1: Congruences
Prepared by:

Joseph Malkevitch
Department of Mathematics and Computing
York College (CUNY)
Jamaica, New York 11451-0001


email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk/



1. Find the value of the ? for the congruences below:

a. 17 ? mod 10

b. 33 ? mod 10

c. 10023223 ? mod 10

d. -12 ? mod 10

e. -69 ? mod 10


2. For each of the congruences below state if it is correct or not:

a. - 15 3 mod 6

b. 45 26 mod 9

c. 39 -1 mod 4

d. -11 -3 mod 4

e. (-3)4 -1 mod 20

f. -42 -2 mod 7

g. 33 2 mod 5



2. Write down the addition and multiplicaton table for the finite arithmetic with 11 elements. Do the elements of this arithmetic form a finite field?

3. Write down the addition and multiplication table for the finite arithmetic with 6 elements. Do the elements of this arithmetic form a finite field? What is this algebraic structure usually called in modern algebra?