Number Theory

1. solving equations

1.1. conditions

1.2. examples

1.3. number of solutions

1.4. new variable floor and arbitrary integers

2. sums of squares

2.1. fermat

2.2. rationals

2.3. general solution

2.4. 4^a(8k+7)

3. primality testing

3.1. fermat's numbers

3.1.1. pepin

3.2. tests

3.2.1. luca

3.2.2. pseudoprimes

3.2.3. miller-rabin

3.2.4. solutions to x^2 = 1 mod n

3.3. carmichael number

4. floor function

4.1. relatively prime results

5. arithmetic functions

6. legendre symbol

6.1. quadratic residue

6.2. Gauss's Lemma

6.3. Euler's Criterion

6.4. law of Quadratic Reciprocity

7. p-adic

7.1. valuations

7.1.1. archimedean

7.1.2. principle of domination

7.1.3. square in Qp