Stony Brook University MAT 118 Spring 2013

Assignment 10 due in Recitation, week of April 15

1. Follow the models given in class and in the notes to write the addition and multiplication tables mod $5$.
• $3 + x \equiv 1$ mod $5$
• $x + 4 \equiv 3$ mod $5$
• $3\cdot x \equiv 1$ mod $5$
• $x \cdot 4 \equiv 3$ mod $5$
4. Write the multiplication table mod $13$.
5. 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 $13$.
6. Use your multiplication table to solve $10\cdot x \equiv 7$ mod $13$.
7. 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.