Journal of Integer Sequences, Vol. 13 (2010), Article 10.1.3 |

Université de Sousse

ISITCOM Hammam Sousse

Dép. de Math Inf.

5 Bis Rue 1 Juin 1955

4011 Hammam Sousse

Tunisie

A. Zekraoui

Université de Monastir

F. S. M.

Dép. de Math.

Avenue de l'environnement

5000 Monastir

Tunisie

**Abstract:**

For
with and
, let
be the unique
subset of
such that
(mod ), where
is the
number of partitions of with parts in . Let be
an odd prime number, and let be irreducible of order ; i.e.,
is the smallest positive integer such that divides
in
. N. Baccar proved that the elements of
of the form , where and is odd,
are given by the -adic expansion of a zero of some polynomial
with integer coefficients. Let be the order of
modulo , i.e., the smallest positive integer such that
(mod ). Improving on the method with which was obtained explicitly only when
, here we make explicit when
. For that, we have used the number of points of the elliptic curve
modulo .

Received July 16 2009;
revised version received December 23 2009.
Published in *Journal of Integer Sequences*, December 31 2009.

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