A new lower bound for the de Bruijn-Newman constant.
A new method to obtain series for and .
A new solution to the equation .
A note on a one-parameter family of Catalan-like numbers.
A note on factorization of the Fermat numbers and their factors of the form
We show that any factorization of any composite Fermat number into two nontrivial factors can be expressed in the form for some odd and , and integer . We prove that the greatest common divisor of and is 1, , and either or , i.e., for an integer . Factorizations of into more than two factors are investigated as well. In particular, we prove that if then and .
A note on integral clock triangles.
A note on the extensions of Eratosthenes' sieve.
A parametric family of elliptic curves
A parametric family of quartic Thue equations
A parametric family of sextic Thue equations
A polynomial reduction algorithm
The algorithm described in this paper is a practical approach to the problem of giving, for each number field a polynomial, as canonical as possible, a root of which is a primitive element of the extension . Our algorithm uses the algorithm to find a basis of minimal vectors for the lattice of determined by the integers of under the canonical map.
A practical version of the generalized Lagrange algorithm.
A problem concerning a character sum.
A procedure to calcute torsion of elliptic curves over Q.
A quadratic field which is euclidean but not norm-euclidean.
A recursive formula for the Kolakoski sequence A000002.
A remark on prime divisors of lengths of sides of Heron triangles.
A sixteenth-order polylogarithm ladder.
A slow-growing sequence defined by an unusual recurrence.
A solution to an “unsolved problem in number theory”.