## Stony Brook University

MAT 118 Spring 2013

### Assignment 10 due in Recitation, week of April 15

- Follow the models given in class and
in the notes to
write the addition and multiplication tables
*mod* $5$.
- Use your addition table to solve
- $3 + x \equiv 1$
*mod* $5$
- $x + 4 \equiv 3$
*mod* $5$

- Use your multiplication table to solve
- $3\cdot x \equiv 1$
*mod* $5$
- $x \cdot 4 \equiv 3$
*mod* $5$

- Write the multiplication table
*mod* $13$.
- Use your multiplication table to identify
the reciprocals (multiplicative inverses) of all
the non-zero equivalence classes
*mod* $13$.
For example the *mod* $13$ reciprocal of $7$
is $2$ since $7\cdot 2 = 14 = 13 + 1$ so
$7\cdot 2 \equiv 1$ *mod* $13$.
- Use your multiplication table to solve
$10\cdot x \equiv 7$
*mod* $13$.
- Use your multiplication to identify all the
*perfect squares* *mod* $13$. These
are the numbers equal to $x\cdot x$ *mod* $13$
for some $x$. You should find seven of them, counting zero.

Remember: Collaboration is fine, but
what you hand in *should be your own work.* Handing in
something you copied is plagiarism and will cost you if it is
detected. Write down what you tried and how it worked.