Elliptic Curves y²=x³-px of Rank Two

A class of prime numbers p is given for which the elliptic curve y² =x³-px has rank two. This extends a theorem of Kudo and Motose.</p

The Prime Ideal Factorization of 2 in Pure Quartic Fields with Index 2

The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicitly.</p

Dihedral Quintic Fields with a Power Basis

It is shown that there exist infinitely many dihedral quintic fields with a power basis.</p

Families of non-congruent numbers with arbitrarily many prime factors

AbstractA method is given for generating families of non-congruent numbers with arbitrarily many prime factors. We then use this method to construct an infinite set of new families of these numbers with prime factors of the form 8k+3

On the Common Index Divisors of a Dihedral Field of Prime Degree

A criterion for a prime to be a common index divisor of a dihedral field of prime degree is given. This criterion is used to determine the index of families of dihedral fields of degrees 5 and 7

INTERSECTIVE POLYNOMIALS WITH GALOIS GROUP D₅

We give an infinite family of intersective polynomials with Galois group D5, the dihedral group of order 10

Cubic fields with a power basis

It is shown that there exist infinitely many cubic fields L with a power basis such that the splitting field M of L contains a given quadratic field K