Archive for August, 2010

Homework problems

August 21, 2010

Let $f_S(g, n)$ count the number of integers $\le n$ that are not expressible as a sum of $g$ elements of $S$.

1) Give me set $S$ for which both $f_S(g, n)$ and $\displaystyle \frac{n}{f_S(g, n)}$ diverge.
2) Proof (or disproof) that, for $S$, we can’t take the set of $k$-th powers, for some $k$

Problem 2) feels really hard, 1) should be fun.