This course will be an introduction to Number Theory from an advanced standpoint. We will study in depth the arithmetic properties of integers, starting with prime factorizations and then investigating implications and generalizations. We will cover the following topics as time permits:

• unique factorization
• congruences, Fermat's Little Theorem, and Euler's Theorem
• primitive roots
• quadratic residues and quadratic reciprocity
• Gauss and Jacobi sums
• cubic and biquadratic reciprocity
• polynomial equations over finite fields and congruence zeta functions
• Pell's equation
• sums of squares