# Elementary number theory
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1. Integers
- natural number
- integer 
- square number
- triangle number
- basis representation theorem
- rational number
- irrational number
2. Divisibility
- divisibility
- even number
- odd number
- Euclid's division lemma
- perfect number
3. Primality
- prime number
- composite number
- sieve of Eratosthenes
- greatest common divisor
- lowest common multiple
- factor
- multiple
- coprime numbers
- Euclidean algorithm
- Bézout's identity
- primorial function
- Euclid's theorem
- Euclid's lemma
- fundamental theorem of arithmetic
- Fermat prime
- Mersenne prime
- properties of Mersenne primes
4. Modular arithmetic
- Fermat's little theorem
- Euler's totient function
- Euler's theorem
- chinese remainder theorem (CRT)
- Lagrange's theorem
- quadratic residue
- Euler's criterion
- Gauss' lemma
- law of quadratic reciprocity
- Wilson's theorem
- uniqueness mod (p-1)/2 of quadratic residues



- tau function
- properties of tau function
- sigma function
- properties of sigma function
- Jordan totient function
- Möbius function 
- Liouville function 
- Carmichael function


- Carmichael numbers