NO-ABEL 2014

The points $P$ and $Q$ lie on the sides $BC$ and $CD$ of the parallelogram $ABCD$ so that $BP = QD$ . Show that the intersection point between the lines $BQ$ and $DP$ lies on the line bisecting $\angle BAD$ .

Find all triples $(a, b, c)$ of positive integers for which $\frac{32a + 3b + 48c}{4abc}$ is also an integer.