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.