Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen

@article{Khnel1950VerschrfungDN,
  title={Versch{\"a}rfung der notwendigen Bedingungen f{\"u}r die Existenz von ungeraden vollkommenen Zahlen},
  author={Ullrich K{\"u}hnel},
  journal={Mathematische Zeitschrift},
  year={1950},
  volume={52},
  pages={202-211}
}
  • Ullrich Kühnel
  • Published 1 December 1950
  • Mathematics
  • Mathematische Zeitschrift
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13 Citations
Highly Influential Citations
1
Background Citations
5

13 Citations

A new result concerning the structure of odd perfect numbers
It is proved here that an odd number of the form paS6, where s is square-free, p is a prime which does not divide s, and p and a are both congruent to 1 modulo 4, cannot be perfect. A positive…
ON ODD PERFECT NUMBERS
In this note, we introduce the notion of the disc induced by an arithmetic function and apply this notion to the odd perfect number problem. We show that under certain special local condition an odd…
Singularities, Supersymmetry and Combinatorial Reciprocity
The First Years
Proving Touchard's Theorem From Euler's Form
This paper derives Touchard's theorem from Euler's form for odd perfect numbers. It also fine-tunes Euler's form.
Perfect numbers: Old and new issues; perspectives
On the number of distinct prime factors of an odd perfect number
Sylvester: Ushering in the Modern Era of Research on Odd Perfect Numbers
In 1888, James Joseph Sylvester (1814-1897) published a series of papers that he hoped would pave the way for a general proof of the nonexistence of an odd perfect number (OPN). Seemingly unaware…
The second largest prime divisor of an odd perfect number exceeds ten thousand
TLDR
The latter bound of the statement in the title of this paper is improved, showing that the largest prime divisor of an odd perfect number must exceed 10 6 , and Hagis showed that the second largest must exceeds 10 3 .
How to Recognize Whether a Natural Number is a Prime
TLDR
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
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References

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The collected mathematical papers
History of the Theory of Numbers
THE third and concluding volume of Prof. Dickson's great work deals first with the arithmetical. theory of binary quadratic forms. A long chapter on the class-number is contributed by Mr. G. H.…