Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen.

  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)},
  pages={146 - 93}
  • E. Kummer
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
Using the Particle Model to Find Structure in Eilenberg-MacLane Spaces
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
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
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
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
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
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
It is proved that every positive integer $n$ has infinitely many multiples with this property.
Lucas numbers of the form (2t/k)
  • N. Irmak, L. Szalay
  • Mathematics
    Acta 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
  • A. Wojda
  • Mathematics
    Discuss. 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
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