Geodesic
FACTORIALS AND THE RAMANUJAN FUNCTION
Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 177-185

Voir la notice de l'article provenant de la source Cambridge University Press

In 2006, F. Luca and I. E. Shparlinski (Proc. Indian Acad. Sci. (Math. Sci.)116(1) (2006), 1–8) proved that there are only finitely many pairs (n, m) of positive integers which satisfy the Diophantine equation |τ(n!)|=m!, where τ is the Ramanujan function. In this paper, we follow the same approach of Luca and Shparlinski (Proc. Indian Acad. Sci. (Math. Sci.)116(1) (2006), 1–8) to determine all solutions of the above equation. The proof of our main theorem uses linear forms in two logarithms and arithmetic properties of the Ramanujan function. 
BRAVO, JHON J.; LUCA, FLORIAN. FACTORIALS AND THE RAMANUJAN FUNCTION. Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 177-185. doi: 10.1017/S0017089515000130
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