Modular Arithmetic

Question 1

What is congruence?

Answer 1

A and B have the same remainder.

3/2 r1
5/2 r1

Question 2

What does this symbol ≡ mean?

Answer 2

congruent/congruence

Question 3

Perform the calculation for 325 x 114 (mod 41).

Answer 3

Step 1: 37050/41 = 903.6
As we’ve proved it’s not an integer we’ll know there’s a remainder

2: 903 x 41 = 37023
times the integer number by the mod number given ‘41’

3: 37050 - 37023 = 27
*this gives our answer *

Question 4

Perform the calculation (43-18) mod 7

Answer 4

1: 25 mod 7 so would be 25/7 = 3.57…
2: 3 x 7 = 21
3: 25 -21
= 4

Question 5

How would you work out multiplicative inverse for 4 mod 7?

Answer 5

4 can’t be divided by 7 so simply x 4 until 7 can go into that number.

1x 4 = 4
2x 4 = 8

So 2 would be the multiplicative inverse.