5

Part of 2002 AIME Problems

Problems(2)

Source:

A_1, A_2, A_3, \ldots, A_{12}

be the vertices of a regular dodecagon. How many distinct squares in the plane of the dodecagon have at least two vertices in the set

\{A_1,A_2,A_3,\ldots,A_{12}\}?

Funky Divisors Problem

Source:

Find the sum of all positive integers

a=2^{n}3^{m},

n

m

are non-negative integers, for which

a^{6}

is not a divisor of

6^{a}.