## Math 310: Review Exam 1

To prepare for Exam 1:
- Be sure to be able to do all
of the homework and quiz problems.
- Be sure you understand my solutions for each
assignment.
- Be sure you've read the first six
chapters of the book.

Here is a link to the first exam I gave the last time I taught M310.

Here are the main topics we've covered:
- Arithmetic modulo m, especially high powers.
- Properties of relations.
- Euclid's algorithm, Bezout's identity and solving linear equations ax + my = b or ax == b (mod m).
- when is there a solution and why
- what are all the solutions and why
- multiplicative inverses modulo m

- Proofs by induction.
- The well-ordering principle.
- Facts about gcd's and lcm's.
- The Fundamental Theorem of Arithmetic.
- Euclid's proof that there are infinitely many primes.
- The prime number theorem