Chapter 2
Modular arithmetic



  1. Arithmetic modulo n

  2. Linear congruences

  3. The a-ary number system

  4. The RSA cryptosystem

  5. Radar detection

  6. Exercises

  7. Summary of Chapter 2


It frequently happens that we prefer to ignore multiples of a given number when we do calculations. Just think of the days in a week or the hours in a day; in the first case we ignore multiples of seven, in the second case multiples of 24. In this chapter we will describe this `arithmetic modulo n'. It will prove to be useful in the discussion of number systems distinct from the decimal system. Other applications are the RSA cryptosystem and a radar detection pattern.

Section 2.1
Arithmetic modulo n
  1. Modular congruence
  2. Addition and multiplication
  3. Multiplicative inverse

Section 2.2
Linear congruences
  1. The notion
  2. Solving linear congruences
  3. Chinese remainder theorem

Section 2.3
The a-ary number system
  1. The notion

Section 2.4
The RSA cryptosystem
  1. Fermat's little theorem
  2. RSA ingredients
  3. Encoding and decoding
  4. How to use RSA

Section 2.5
Radar detection
  1. Detection pattern
  2. Primitive elements
  3. Pattern construction