Summary of Chapter 2

Overview of sections

1. Arithmetic modulo n
2. Linear congruences
3. The a-ary number system
4. The RSA cryptosystem
5. Radar detection
6. Exercises

Overview of contents

In Z/nZ, the quotient ring modulo n, one can

• add, subtract,
• multiply,
• divide 1 by a provided gcd(a,n) = 1; the result is called the inverse of a.

For these new rings we have looked at

• linear congruences,
• Chinese remainder theorem,
• Fermat's little theorem, which was useful for:
• cryptography (RSA),
• for n prime: primitive elements, these are elements whose powers form the entire set (Z/nZ)\{0}.