Question

Find all replacements (less than the modulus. for the question mark that make the statement true. 5 + 5 ≡ ? (mod 6)


A. 0

B. 1

C. 2

D. 4

Answer 1

We know:
\[
\begin{align}
5&\equiv-1\mod 6\implies\\
-1+-1&\equiv-2\mod 6\implies\\
-2+6&\equiv-2+0\mod 6\implies\\
4&\equiv-2\equiv5+5\mod 6
\end{align}
\]And we are done.