Geodesic
On Sierpinski's Conjecture Concerning the Euler Totient
Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 401-404

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

If Φk(n) denotes the Schemmel totient (so that Φ1 (n) becomes the Euler totient) we conjecture that for each k ≥ 1 and any given integer n > 1 there exist infinitely many m for which the equation Φk (x) = m has exactly n solutions. For the case k = 1, this gives Sierpinski's conjecture.We prove that on the basis of Schinzel's Hypothesis H, our conjecture holds for any k ≥ 3 of the form where p0 is an odd prime and α ∊ N. In 1961 Schinzel proved the case k = 1 assuming his Hypothesis H. 
Subbarao, M. V. On Sierpinski's Conjecture Concerning the Euler Totient. Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 401-404. doi: 10.4153/CMB-1991-064-3
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