Question

$-41 \mod 9$ is

• A. 5
• B. 4
• C. 3
• D. 0

Hint:

When taking mod of a negative number, always find the equivalent positive remainder between $0$ and $n-1$.

Answer 1

The Correct Option is A

To compute $-41 \mod 9$, we look for the smallest non-negative remainder when $-41$ is divided by $9$.
We know that $-41 = -5 \times 9 + 4$, but this gives a remainder of $4$, which doesn't satisfy the modular definition.
Instead, we adjust the result to ensure a positive remainder.
$-41 \mod 9 = 9 - (|{-41}| \mod 9) = 9 - (5) = 4$ is incorrect.
The correct method is to find a number $r$ such that $-41 \equiv r \pmod{9}$ and $0 \leq r<9$.
Now, $-41 \equiv 5 \pmod{9}$, since $-41 + 46 = 5$ and $46$ is a multiple of $9$.
Thus, the correct remainder is 5.