Metamath Proof Explorer

Table of Contents - 6. ELEMENTARY NUMBER THEORY

Here we introduce elementary number theory, in particular the elementary properties of divisibility and elementary prime number theory.

1. Elementary properties of divisibility
   1. Irrationality of square root of 2
   2. Some Number sets are chains of proper subsets
   3. The divides relation
   4. Even and odd numbers
   5. The division algorithm
   6. Bit sequences
   7. The greatest common divisor operator
   8. Bézout's identity
   9. Algorithms
   10. Euclid's Algorithm
   11. The least common multiple
   12. Coprimality and Euclid's lemma
   13. Cancellability of congruences
2. Elementary prime number theory
   1. Elementary properties
   2. Coprimality and Euclid's lemma (cont.)
   3. Properties of the canonical representation of a rational
   4. Euler's theorem
   5. Arithmetic modulo a prime number
   6. Pythagorean Triples
   7. The prime count function
   8. Pocklington's theorem
   9. Infinite primes theorem
   10. Sum of prime reciprocals
   11. Fundamental theorem of arithmetic
   12. Lagrange's four-square theorem
   13. Van der Waerden's theorem
   14. Ramsey's theorem
   15. Primorial function
   16. Prime gaps
   17. Decimal arithmetic (cont.)
   18. Cyclical shifts of words (cont.)
   19. Specific prime numbers
   20. Very large primes