tauraso22. 152KB Jun 04 2011 12:09:36 AM
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2
3
47
6
Journal of Integer Sequences, Vol. 13 (2010),
Article 10.5.1
23 11
Congruences of Multiple Sums Involving
Sequences Invariant Under the Binomial
Transform
Sandro Mattarei
Dipartimento di Matematica
Universit`a di Trento
via Sommarive, 14
38100 Trento, Italy
[email protected]
Roberto Tauraso
Dipartimento di Matematica
Universit`a di Roma “Tor Vergata”
via della Ricerca Scientifica
00133 Roma, Italy
[email protected]
Abstract
We prove several congruences modulo a power of a prime, such as
n+1
2
+2
− n+1 p Bp−n−1 (1/3) (mod p2 ), if n is odd,
X
p − kn (−1)kn
6
≡
n+1 + 4
3
k1 · · · kn
2
0
2
3
47
6
Journal of Integer Sequences, Vol. 13 (2010),
Article 10.5.1
23 11
Congruences of Multiple Sums Involving
Sequences Invariant Under the Binomial
Transform
Sandro Mattarei
Dipartimento di Matematica
Universit`a di Trento
via Sommarive, 14
38100 Trento, Italy
[email protected]
Roberto Tauraso
Dipartimento di Matematica
Universit`a di Roma “Tor Vergata”
via della Ricerca Scientifica
00133 Roma, Italy
[email protected]
Abstract
We prove several congruences modulo a power of a prime, such as
n+1
2
+2
− n+1 p Bp−n−1 (1/3) (mod p2 ), if n is odd,
X
p − kn (−1)kn
6
≡
n+1 + 4
3
k1 · · · kn
2
0