## Rigorous Elementary Mathematics

Existsforall Academy presents a 4-volume series of books: Rigorous Elementary Mathematics, authored by Samer Seraj. The theme of the books is the rigorous proof of many results that are often learned by students without proof in elementary mathematics, specifically algebra, counting, number theory, and geometry. The books were written for students of mathematical contests and olympiads who want to add a rigorous foundation to their understanding of the theorems that they use, and for teachers and coaches who want to solidify their own fundamentals. **To download the books, click on the cover photos.** The tables of contents are provided below as a preview. To stay up to date on further projects, please sign up for the academy’s Newsletter. You might also be interested in my research Publications.

##### Volume 3: Number Theory

ISBN 978-1-7389501-2-6

- Divisibility
- Primes
- Arithmetic Functions
- Modular Arithmetic
- Diophantine Analysis
- Linear Diophantine Equations
- Base Representations I
- Combinatorial Expressions
- Modular Exponentiation
- Base Representations II
- Modular Power Residues
- Special Forms of Integers
- Difference and Sum of Powers