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Non‐linear Transformations of Divergent and Slowly Convergent Sequences
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 theExpand
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Solved and Unsolved Problems in Number Theory
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 withExpand
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Strong primality tests that are not sufficient
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 aExpand
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Quadratic Residues and the Distribution of Primes
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
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On the Distribution of Parity in the Partition Function
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 thatExpand
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The simplest cubic fields
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 AExpand
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On maximal gaps between successive primes
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 ourExpand
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Variations on a theorem of Landau. I
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On Gauss’s class number problems
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 suchExpand
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