basic modulus question

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 $51$?

Please read this tutorial on how to typeset mathematics on this site. — N. F. Taussig, May 29 '16 at 10:38
Otherwise said: $a$ and $b$ have the same remainder when $a$ and $b$ are divided by $n$. What you mention is denoted by $a=b\bmod n$ (note no parentheses, equality symbol and the smaller distance between $b$ and $\mod{}$). TeX code:\bmod`. — Bernard, May 29 '16 at 10:41

score 0 · Accepted Answer · answered May 29 '16 at 10:38

0

$41 \pmod 5 \equiv1\pmod5$ (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: $41\equiv 51 \pmod 5$.

$$a\equiv1\pmod5$$

$$b\equiv1\pmod5$$

answered May 29 '16 at 10:38

anonymous

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basic modulus question

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