We use a connection between the arithmetic of elliptic curves of the form y² = x³ + k and the arithmetic of the quadratic number fields Q(√k) and Q(√-3k) to look for quadratic fields with high ...

This is a preview. Log in through your library . Abstract In a quadratic number field $\mathbf{Q}(\sqrt D), D$ a squarefree integer, with class number 1, any algebraic integer can be decomposed ...

There are three kinds of prime numbers. The first is a solitary outlier: 2, the only even prime. After that, half the primes leave a remainder of 1 when divided by 4. The other half leave a remainder ...