Assessment -Modular Arithmetic

EQUATION OF MODULO

Solve the following equations in their giving moduli

1. 3x =5mod 7 2x + 3 =1 mod 6   c.

SOLUTION

1. 3x =5+7 ,. 3x =12

X = 4 mod 7

1. 2x +3 =1+6 , 2x +3  =7

2x 7 -5, then   2x  = 4

X =2 mod 6

ASSESSMENT: Solve the following questions;

1. Use the cycle number in modulo 6 to simplify the following.

• 2 + 10 (ii). 5 + 5  (iii) 15 + 37 (iv) 2 – 9  (v) 0 – 22

2. A toy car starts at a point 0 and runs around a circular track of 2 meters. How far is the car from its starting point along the track when it has gone :

• 6m (b) 15m (c) 21m (d) 87m

3. Find the following numbers in their simplest form in modulo 4:

(i). 62(ii). 102 (iii) -56 (iv) -78 (v) -202