This paper discusses a family of non-linear sequence-to-sequence transformations designated as ek, ekm, ẽk, and ed. A brief history of the transforms is related and a simple motivation for the… Expand

When writing can change your life, when writing can enrich you by offering much money, why don't you try it? Are you still very confused of where getting the ideas? Do you still have no idea with… Expand

A detailed investigation is given of the possible use of cubic recurrences in primality tests. No attempt is made in this abstract to cover all of the many topics examined in the paper. Define a… Expand

Since\/?i/log n —» oo, ir~(n) could thus be made to exceed ir+(n) by any amount by an appropriate choice of n. This theorem (which was one of the above-mentioned three senses) was proven by Phragmén,… Expand

Kolbcrg [1] proved, but by contradiction and without identifying the arguments n, that i nitely many p(n) are even, and infinitely many are odd. His proof is almost as simple as Euclid's proof that… Expand

Abstract. The cyclic cubic fields generated by x3 = ax2 + (a + 3)x + 1 are studied in detail. The regulators are relatively small and are known at once. The class numbers are al2 2 ways of the form A… Expand

exists and perhaps it might be possible to determine its value, but it will probably not be possible to express ft(n) by a simple function of n and t (even for t = 3). If t is large compared to n our… Expand

Let h be the class number of binary quadratic forms (in Gauss's formulation). All negative determinants having some h = 6n i: 1 can be deter- mined constructively: for h = 5 there are four such… Expand