Find each of these values.

a) (177 mod 31 + 270 mod 31) mod 31

b) (177 mod 31 · 270 mod 31) mod 31

Step 1</p>

Here, in this problem we have to find values of addition of two modulus.

To calculate the values, either we can calculate individually and add or we can use formula which states that, if a and b be integers and m be a positive integer.

then,

.

and

Step2

a) (177 mod 31 + 270 mod 31) mod 31

Here, we have a = 177, b = 270 and m = 31

Using formula,

We have,

=447 mod 31

We can write

Therefore, 447 mod 31 = 13

Therefore value of (177 mod 31 + 270 mod 31) mod 31 is 13.