Question

How (-1) mod 5 is equal to 9?

Answer 1

-1(mod 5)

`- ve * 5 + \: + ve = - 1 \\ - 1 * 5 + 4 = - 1 \\ 4(mod \: 5)`

The positive value added will be the new number .

Answer 2

see below

Explanation:

when we say a≡b mod c

it means that c divides a-b

or that b is the remainder of a/c

so 9/5 the remainder is 4

so we have

9≡4 mod 5

we can substract 5 from both sides and the equation will still be true

9-5≡4-5 mod 5

4≡1 mod 5

if we do it by c divides a-b

5 divides 9-(-1)

5 divides 10

which is true so

9≡-1 mod 5