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Problems for Chapter VI
Problems for Chapter VI
1. Prove, by elementary methods, that there are infinitely many
primes not ending in the digit 1.
2. Prove that there are infinitely many primes p for which neither
p + 2 nor p − 2 is prime.
3. Prove that at least 1/6 of the integers are not expressible as the
sum of 3 squares.

4. Prove that A(z) has no zeros in the whole plane, although, it has
poles.

5. Suppose δ(x) decreases to 0 as x →∞. Produce an ε(x) which
goes to 0 at ∞ but for which δ(xε(x)) o(ε(x)).