# 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}
}
• E. Kummer
• Journal für die reine und angewandte Mathematik (Crelles Journal)
177 Citations
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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