# Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen.

@article{KummerberDE, title={{\"U}ber die Erg{\"a}nzungss{\"a}tze zu den allgemeinen Reciprocit{\"a}tsgesetzen.}, author={Ernst Eduard Kummer}, journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)}, volume={1852}, pages={146 - 93} }

## 177 Citations

Using the Particle Model to Find Structure in Eilenberg-MacLane Spaces

- Mathematics
- 2021

We introduce two models, the bar construction and the particle model, for a collection of spaces known as Eilenberg-MacLane spaces. These spaces can be used as building blocks for other spaces and…

Divisibility of binomial coefficients by powers of primes

- Mathematics
- 2016

For a prime $p$ and nonnegative integers $j$ and $n$ let $\vartheta_p(j,n)$ be the number of entries in the $n$-th row of Pascal's triangle that are exactly divisible by $p^j$. Moreover, for a finite…

A method for constructing groups of permutation polynomials and its application to projective geometry

- Mathematics
- 2015

This dissertation presents original work on permutation polynomials over finite fields. From a consideration of the proof of Cayley’s theorem, it is clear that any finite group can be represented as…

Higher Degree Davenport Constants over Finite Commutative Rings

- Mathematics
- 2021

We generalize the notion of Davenport constants to a ‘higher degree’ and obtain various lower and upper bounds, which are sometimes exact as is the case for certain finite commutative rings of prime…

Ranks of Quotients, Remainders and $p$-Adic Digits of Matrices

- MathematicsArXiv
- 2014

Upper bounds are proven for the $\mathbb{Z}/p p A/A/p Z-rank of A for all $i \ge 0$ when $p = 2$, and a conjecture is presented for odd primes.

Binomial Coefficient Predictors

- Mathematics
- 2011

For a prime p and nonnegative integers n, k, consider the set A (p) n,k = {x ∈ [0, 1, ..., n] : p|| ( n x ) }. Let the expansion of n + 1 in base p be n + 1 = α0p ν + α1p ν−1 + · · · + αν , where 0 ≤…

On the divisibility of binomial coefficients

- MathematicsArs Math. Contemp.
- 2020

It is proved that every positive integer $n$ has infinitely many multiples with this property.

Lucas numbers of the form (2t/k)

- MathematicsActa et Commentationes Universitatis Tartuensis de Mathematica
- 2019

Let Lm denote the mth Lucas number. We show that the solutions to the diophantine equation (2t/k) = Lm, in non-negative integers t, k ≤ 2t−1, and m, are (t, k, m) = (1, 1, 0), (2, 1, 3), and (a, 0,…

Almost Self-Complementary Uniform Hypergraphs

- MathematicsDiscuss. Math. Graph Theory
- 2018

It is proved that an almost self-complementary k-hypergraph of order n exists if and only if (nk) $\left({ n \cr k \cr } } \right)$ is odd.

Structure and asymptotics for Catalan numbers modulo primes using automata

- Mathematics
- 2017

Let Cn be the nth Catalan number. We show that the asymptotic density of the set {n : Cn ≡ 0 mod p} is 1 for all primes p, We also show that if n = pk−1 then Cn ≡ −1 mod p. Finally we show that if n…