What is the value of (-17 \times 5) \pmod{6} expressed in standard non-negative remainder … — JAMB UTME

What is the value of $(-17 \times 5) \pmod{6}$ expressed in standard non-negative remainder form?

5

Multiplying

-17

5

yields

-85

. When

-85

is divided by

6

, the closest multiple of

6

below

-85

-90

. The non-negative remainder is

-85 - (-90) = 5

, which belongs to the canonical set

\{0, 1, 2, 3, 4, 5\}

Multiply the numbers inside the parentheses

-17 \times 5 = -85

Perform standard multiplication before applying the modulo operation.

Express the negative number in terms of the modulus 6

-85 = 6 \times (-15) + 5

Find the largest multiple of 6 less than or equal to -85, which is -90.

Extract the canonical non-negative remainder

5

In standard modular arithmetic, remainders must lie in the range

[0, n-1]

, where

n

is the modulus.

Modular Arithmetic and Non-Negative Remainders

Question