A new formulation of the law of octic reciprocity for primes =+-3 (mod 8) and its consequences.
A divisibility property of binomial coefficients viewed as an elementary sieve.
On the Lagrange resolvents of a dihedral quintic polynomial.
A relative integral basis over for the normal closure of a pure cubic field.
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).
Note on a Cubic Character Sum.
3 as a Ninth Power (mod p).
Forms Representable by an Integral Positive-Definite Binary Quadratic Form.
Note on a result of Barrucand and Cohn.
Explicit forms of Kummer's complementary theorems to his law of quintic reciprocity.
Quadratic forms and a product-to-sum formula
Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4
Under the assumption that the ternary form x² + 2y² + 5z² + xz represents all odd positive integers, we prove that a ternary quadratic form ax² + by² + cz² (a,b,c ∈ ℕ) represents all positive integers n ≡ 4(mod 8) if and only if it represents the eight integers 4,12,20,28,52,60,140 and 308.
On the least quadratic non-residue of a prime p ... 3 (mod 4).
Determination of modulo p
Some new evaluations of the Legendre symbol ((a+b√q)/p)
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.
An arithmetic formula of Liouville
An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.
Ramanujan identities and Euler products for a type of Dirichlet series
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