A congruence of Emma Lehmer (1938) for Euler numbers 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 play an important role, and we present some numerical results.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-1-4,
author = {John B. Cosgrave and Karl Dilcher},
title = {On a congruence of Emma Lehmer related to Euler numbers},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {47-67},
zbl = {1325.11004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-1-4}
}
John B. Cosgrave; Karl Dilcher. On a congruence of Emma Lehmer related to Euler numbers. Acta Arithmetica, Tome 161 (2013) pp. 47-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-1-4/