basic modulus question So if so $a \equiv b \pmod{n}$, which should be read as "$a$ is congruent to $b$ modulo $n$" which from what I understand is something among the lines of "$a$ is the remainder when $b$ is divided by $n$".
Now, given $51 \equiv 41 \pmod{5}$ means the remainder of $41$ divided by $5$ is $1$, so this is $a$? I am confused as a looks to be $51$?

$41 \pmod 5 \equiv1\pmod5$ (This is $\frac{41}{5}, $ with a remainder of $1.$)
$51 \pmod 5 \equiv1\pmod5$ (This is $\frac{51}{5}, $ also with a remainder of $1.$)
Therefore: $41\equiv 51 \pmod 5$.
$$a\equiv1\pmod5$$
$$b\equiv1\pmod5$$
