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5 votes
3 answers
829 views

Is the number of solutions of $\phi(x)=n!$ bounded? If yes, what is its bound?

Pillai showed in 1929 that the function $A(n)$ giving the number solutions of the equation $\phi(x)=n$ is unbounded in (S. Pillai, On some functions connected with $\varphi(n)$, Bull. Amer. Math. Soc. …
0 votes
2 answers
103 views

Is this $a(p)=\lim_{r\to \infty} \frac{VolS(p,r)}{e^{h r}}$ exists and applied for manifolds...

In $1969$, Margulis proved, for suitable constant $h>0$and $r$ is a positive constant that : $a(p)=\lim_{r\to \infty} \frac{VolS(p,r)}{e^{h r}}$ with ($(S(p,r)$ is geodesic spheres), exists at each …