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The divisibility of isols by powers of primes

✍ Scribed by J. C. E. Dekker; J. Myhill

Publisher
Springer-Verlag
Year
1960
Tongue
French
Weight
272 KB
Volume
73
Category
Article
ISSN
0025-5874

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πŸ“œ SIMILAR VOLUMES

Integers divisible by sums of powers of
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✍ Jean-Marie De Koninck; Florian Luca πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 115 KB

For each positive integer j , let β j (n) := p|n p j . Given a fixed positive integer k, we show that there are infinitely many positive integers n having at least two distinct prime factors and such that β j (n) | n for each j ∈ {1, 2, . . . , k}.

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Divisibility by 2-Powers of Certain Quad
Divisibility by 2-Powers of Certain Quadratic Class Numbers
✍ P. Stevenhagen πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 726 KB

We study the divisibility of the strict class numbers of the quadratic fields of discriminant \(8 p,-8 p\), and \(-4 p\) by powers of 2 for \(p \equiv 1 \bmod 4\) a prime number. Various criteria for divisibility by 8 are discussed, and an analogue of the relation \(8\left|h_{x_{p}} \Leftrightarrow