Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics
Explicit normal integral bases are given for some cyclic quintic fields defined by Emma Lehmer’s parametric family of quintics.
The conductor of a cyclic quartic field using Gauss sums
Let denote the field of rational numbers. Let be a cyclic quartic extension of . It is known that there are unique integers , , , such that where The conductor of is , where A simple proof of this formula for is given, which uses the basic properties of quartic Gauss sums.
Predictive criteria for the representation of primes by binary quadratic forms
Pascal's triangle (mod 9)
On the prime factors of non-congruent numbers
We give infinitely many new families of non-congruent numbers where the first prime factor of each number is of the form 8k+1 and the rest of the prime factors have the form 8k+3. Products of elements in each family are shown to be non-congruent.
PSL septimic fields with a power basis
We give an infinite set of distinct monogenic septimic fields whose normal closure has Galois group .
On the Lagrange resolvents of a dihedral quintic polynomial.
A relative integral basis over for the normal closure of a pure cubic field.
On a sequence of nonsolvable quintic polynomials.
Explicit decomposition of a rational prime in a cubic field.
On the common index divisors of a dihedral field of prime degree.
Cyclotomy of order 15 over , (mod 15).
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