Sets with Even Partition Functions and 2-adic Integers II
Université de Sousse
ISITCOM Hammam Sousse
Dép. de Math Inf.
5 Bis Rue 1 Juin 1955
4011 Hammam Sousse
Université de Monastir
F. S. M.
Dép. de Math.
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be the unique
number of partitions of
with parts in
an odd prime number, and let
be irreducible of order
is the smallest positive integer such that
. N. Baccar proved that the elements of
of the form
are given by the
-adic expansion of a zero of some polynomial
with integer coefficients. Let
be the order of
, i.e., the smallest positive integer such that
). Improving on the method with which
was obtained explicitly only when
, here we make explicit
. For that, we have used the number of points of the elliptic curve
Full version: pdf,
Received July 16 2009;
revised version received December 23 2009.
Published in Journal of Integer Sequences, December 31 2009.
Journal of Integer Sequences home page