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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Number of divisors which are at most $n$
I am going to prove that $\tau_n$ is surjective for $n$ large enough.
Denote by $P_n$ the set of primes $\le n$.
$\tau_n(x)$ depends only on powers of primes from $P_n$ in the decomposition of $x$.
Di …