4. Binary Quadratic Forms

@inproceedings{4BQ,
  title={4. Binary Quadratic Forms},
  author={}
}
    4.1. What integers are represented by a given binary quadratic form?. An integer n is represented by the binary quadratic form ax 2 + bxy + cy 2 if there exist integers r and s such that n = ar 2 + brs + cs 2. In the seventeenth century Fermat showed the first such result, that the primes represented by the binary quadratic form x 2 +y 2 are 2 and those primes ≡ 1 (mod 4), and thence determined all integers that are the sum of two squares (see exercises 4.1a and 4.1b). One can similarly ask for… CONTINUE READING