Dirichlet's Theorem on arithmetic progressions states that there are infinitely many primes of the form
Being $a$ and $b$ coprimes.
- Very elemental question: Can we say that this Theorem:
is equivalent to Dirichlet's one? I supose it is, as it would be the same as $a(n-1)+(n-b)$, but I would like to get sure, as I am not used to work with this kind of formulae
- For which functions $f(n)$ can we say that there are infinitely many primes of the form
$$a[f(n)]+b$$ ? For example, $a2^n+b$ or $a(5n)+b$