# How do you write something in mod form?

I was given the question: A band of 17 pirates has stolen a chest of gold coins. When they try to divide the coins into equal portions, 3 coins are left over.

Could this then be written as $z \equiv 17 \mbox{ mod } 3$?

• It's actually $3\pmod{17}$. One way to think of it is, when you divide the number of coins by $17$, there are $3$ left over. – Edward Jiang Nov 12 '15 at 3:50

You can write it as congruence $$z \equiv 3 \pmod{17}$$ meaning the left hand side having the same remainder like the right hand side, under division by $17$ or via the modulo operator $$z \bmod 17 = 3$$ stating the remainder.
Did you mean $z \equiv 3 \pmod{17}$?
Yes, of course, meaning that $z$ gives remainder $3$ when divided by $17$.
Therefore you'll have $z=3+17k$ , being $k$ an integer number.