# September 29, 2016

Today we worked on the problems from the 2010 Putnam Exam (handed out a couple of weeks ago). We had quite a good time, working in small groups.

Different people worked on different problems, and every problem was tried by at least one person. The only one we presented at the front was problem A1.

• A4: It is a good idea to try to find a nontrivial divisor when $$n=1$$, we may be able to get inspiration from that.
• A5: What does it mean for $$G$$. to be a group with operation $$\ast$$?
• A6: In general, to show that the integral of a positive function $$h(x)$$ diverges it is useful to compare it a function $$g(x)$$ such that $$h(x) \ge g(x) \ge 0$$ and the integral of $$g(x)$$ diverges.
• B1: First we need to make a reasonable guess regarding whether it is possible or not to find such a sequence. Notice that if $$a>1$$ then $$a^m$$ increases as $$m$$ increases, but the opposite happens when $$0<a<1$$.
• We need to be careful when showing that $$k$$ is the maximum value for which something is possible: it does not suffice to be convinced that we have found the maximum, we need to prove that it is in fact the maximum.