Handout - MTH 4390/4590




A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Inverses Mod 26

x 1 3 5 7 9 11 15 17 21 23 25
x$^{-1}$ 1 9 21 15 3 19 7 23 5 17 25

Determine if two numbers are relatively prime

Use the [gcd( ] command on the TI-83/84 calculator.

Example $\gcd (45,12)$

Hit [MATH] [NUM] [gcd( ] [ENTER] (or [MATH] [NUM] [9 ]) 45,12) [ENTER]

This gives 3.

Modular Arithmetic

$y=x$ mod $n$

To compute the remainder $y$ on the TI-83/84 calculators do the following:

Example $y=x$ mod $26$

Hit [y =]. Enter for y1:

y1 = x - [MATH] [NUM] [int( ] [ENTER] x/26)*26 [2nd] [QUIT]

To compute $y=574$ mod $26:$

Hit [VARS] [YVARS] [FUNCTION] [Y1] (574) [ENTER]

This gives $y=2.$ So $574=2$ mod $26.$

Example $y=x$ mod $251$

Hit [y =]. Enter for y1:

y1 = x - [MATH] [NUM] [int( ] [ENTER] x/251)*251 [2nd] [QUIT]

To compute $y=1389$ mod $251:$

Hit [VARS] [YVARS] [FUNCTION] [Y1] (1389) [ENTER]

This gives $y=134.$ So $1389=134$ mod $251.$