Congruences for sequences similar to Euler numbers

AbstractFor a≠0 we define {En(a)} by ∑k=0[n/2](n2k)a2kEn−2k(a)=(1−a)n (n=0,1,2,…), where [n/2]=n/2 or (n−1)/2 according as 2|n or 2∤n. In the paper we establish many congruences for En(a) modulo prime powers, and show that there is a set X and a map T:X→X such that (−1)nE2n(a) is the number of fixed points of Tn

Multiple harmonic sums H{s}2l=1;p−1\mathcal{H}_{\lbrace s\rbrace^{2l}=1;p-1} modulo p4p^4 and applications

Wilson's theorem for the factorial got generalized to the moduli $p^2$ in 1900 and $p^3$ in 2000 by J.W.L. Glaisher and Z-H. Sun respectively. This paper which studies more generally the multiple harmonic sums $\mathcal{H}_{\lbrace s\rbrace^{2l}=1;p-1},2\leq 2l\leq p-1$ modulo $p^4$ in association with the Stirling numbers $\left[\begin{array}{l}\;\;\;p\\2s-1\end{array}\right], 2\leq 2s\leq p-1$ modulo $p^4$ is concerned with establishing a generalization of Wilson, Glaisher and Sun's results to the modulus $p^4$. We also break p-residues of convolutions of three divided Bernoulli numbers of respective orders $p-1$, $p-3$ and $p-5$ into smaller pieces and generalize some results of Sun for some of the generalized harmonic numbers of order $p-1$ modulo $p^4$.Comment: 38 pages; 2 appendices; Published version with minor calculation mistake correcte

A survey of results on Giuga's conjecture and related conjectures.

No abstract available.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b130199