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

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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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     title = {On {Sierpinski's} {Conjecture} {Concerning} the {Euler} {Totient}},
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     year = {1991},
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     doi = {10.4153/CMB-1991-064-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-064-3/}
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