¹University of Brest, Brest, France. Email: Luis.Gallardo@univ-brest.fr

Some formulae of Niebur and Lanphier are derived in an elementary manner from previously known formulae. A new congruence formula for τ(p) modulo p is derived as a consequence. We use this congruence to numerically investigate the order of τ(p) modulo p.

Key words: Ramanujan's tau formulae, Congruences.

Obtenemos algunas fórmulas de Niebur y Lanphier de manera elemental a partir de formulas conocidas. Deducimos una nueva fórmula para la congruencia τ(p) modulo p. Utilizamos esa fórmula para estudiar numéricamente el orden multiplicativo de τ(p) modulo p.

Palabras clave: Fórmulas para la función tau de Ramanujan, congruencias.

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