On a congruence of Emma Lehmer related to Euler numbers

John B. Cosgrave, and Karl Dilcher. "On a congruence of Emma Lehmer related to Euler numbers." Acta Arithmetica 161.1 (2013): 47-67. <http://eudml.org/doc/286382>.

@article{JohnB2013,
abstract = {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.},
author = {John B. Cosgrave, Karl Dilcher},
journal = {Acta Arithmetica},
keywords = {congruences; Euler numbers; sums of reciprocals},
language = {eng},
number = {1},
pages = {47-67},
title = {On a congruence of Emma Lehmer related to Euler numbers},
url = {http://eudml.org/doc/286382},
volume = {161},
year = {2013},
}

TY - JOUR
AU - John B. Cosgrave
AU - Karl Dilcher
TI - On a congruence of Emma Lehmer related to Euler numbers
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 1
SP - 47
EP - 67
AB - 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.
LA - eng
KW - congruences; Euler numbers; sums of reciprocals
UR - http://eudml.org/doc/286382
ER -