On a congruence of Emma Lehmer related to Euler numbers

• Autorzy: John B. Cosgrave , Karl Dilcher
• Języki publikacji: EN

Abstrakty

EN

A congruence of Emma Lehmer (1938) for Euler numbers $E_{p-3}$ modulo p in terms of a certain sum of reciprocals of squares of integers was recently extended to prime power moduli by T. Cai et al. We generalize this further to arbitrary composite moduli n and characterize those n for which the sum in question vanishes modulo n (or modulo n/3 when 3|n). Primes for which $E_{p-3} ≡ 0 (mod p)$ play an important role, and we present some numerical results.

Kategorie tematyczne

• 11B68: Bernoulli and Euler numbers and polynomials
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 1
• Strony: 47-67

Daty

wydano

2013

Twórcy

autor

John B. Cosgrave

• 79 Rowanbyrn, Blackrock, County Dublin, Ireland

autor

Karl Dilcher

• Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

Identyfikatory

DOI

10.4064/aa161-1-4