- Use terms of the continued fraction expansion of to find a solution to Pell’s equation .
- Calculate the Bernoulli number .
- Check that the Bernoulli number formula for gives the usual formula .
- Use the functional equation for the Riemann zeta function to calculate .
- If P1 and P2 are disjoint sets of primes and if both have a well-defined Dirichlet density, then show that densities satisfy d(P1+P2) = d(P1)+d(P2).
- If P is a finite set of primes, show that it has Dirichlet density 0.