An introduction to number theory at the undergraduate level, with the primary focus on examples and proofs that are completely explained. The first few chapters presume familiarity with elementary school algebra, and the exercises, along with their solutions, have been incorporated within the book. Following this, fundamental concepts about groups and rings are used to investigate groups of units, quadratic residues, and arithmetic functions, all of which have applications in enumeration and encryption.
The final section, which is appropriate for students in their third year, investigates the Dirichlet series and sums of squares by applying concepts from algebra, analysis, calculus, and geometry. In particular, the final chapter offers a condensed explanation of Fermat’s Last Theorem, beginning with its discovery in ancient Babylonian and Greek research on Pythagorean triples and ending with the most current proof of the theorem, which Andrew Wiles developed.
