How to Solve $-31 \bmod 11$

Question

How $-31 \bmod 11$ is computing?

I usually get stuck when it comes to negative integer.

How to handle these types of questions?

Answer 1

Let $x = -31 \pmod {11}$

We know $0 = 33 \pmod {11}$

Adding these we get $x = 2 \pmod {11}$

The moral is, just add multiples of your mod until you get a positive number, and you will get the right answer.