Geodesic
On a congruence of Emma Lehmer related to Euler numbers
John B. Cosgrave 1   ; Karl Dilcher 2
1 79 Rowanbyrn Blackrock, County Dublin, Ireland
2 Department of Mathematics and Statistics Dalhousie University Halifax, NS, B3H 3J5, Canada
Acta Arithmetica, Tome 161 (2013) no. 1, pp. 47-67 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $E_{p-3}\equiv 0\pmod{p}$ play an important role, and we present some numerical results.
DOI : 10.4064/aa161-1-4
Keywords: congruence emma lehmer euler numbers p modulo nbsp terms certain sum reciprocals squares integers recently extended prime power moduli nbsp cai generalize further arbitrary composite moduli characterize those which sum question vanishes modulo nbsp modulo primes which p equiv pmod play important role present numerical results

John B. Cosgrave  1   ; Karl Dilcher  2

1 79 Rowanbyrn Blackrock, County Dublin, Ireland
2 Department of Mathematics and Statistics Dalhousie University Halifax, NS, B3H 3J5, Canada 
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John B. Cosgrave; Karl Dilcher. On a congruence of Emma Lehmer related to Euler numbers. Acta Arithmetica, Tome 161 (2013) no. 1, pp. 47-67. doi: 10.4064/aa161-1-4

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