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Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
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Kevin A. Broughan
Veröffentlicht/Copyright:
5. November 2010
Abstract
We show that the set of composite positive integers n ≤ x satisfying the congruence
is of cardinality at most x as x → ∞.
Received: 2009-06-09
Revised: 2010-03-16
Accepted: 2010-05-11
Published Online: 2010-11-05
Published in Print: 2010-November
© de Gruyter 2010
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Artikel in diesem Heft
- Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
- On the Iteration of a Function Related to Euler's φ-Function
- An Explicit Evaluation of the Gosper Sum
- On the Frobenius Problem for {ak, ak + 1, ak + a, . . . , ak + ak−1}
- Generalizing the Combinatorics of Binomial Coefficients via -Nomials
- Finding Almost Squares V
- On Relatively Prime Subsets and Supersets
- Reformed Permutations in Mousetrap and Its Generalizations
- On Ternary Inclusion-Exclusion Polynomials
- Sums and Products of Distinct Sets and Distinct Elements in ℂ
Schlagwörter für diesen Artikel
Wolstenholme's theorem;
binomial congruences;
density zero
Artikel in diesem Heft
- Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
- On the Iteration of a Function Related to Euler's φ-Function
- An Explicit Evaluation of the Gosper Sum
- On the Frobenius Problem for {ak, ak + 1, ak + a, . . . , ak + ak−1}
- Generalizing the Combinatorics of Binomial Coefficients via -Nomials
- Finding Almost Squares V
- On Relatively Prime Subsets and Supersets
- Reformed Permutations in Mousetrap and Its Generalizations
- On Ternary Inclusion-Exclusion Polynomials
- Sums and Products of Distinct Sets and Distinct Elements in ℂ