Archive | September 2010

# Putnam

Let $a_1, a_2, . . . , a_n$ be real numbers, and let $b_1, b_2, ..., b_n$ be distinct positive integers. Suppose that there is a polynomial f(x) satisfying the identity
$(1 - x)^n f(x) = 1 + \sum _{i=1} ^n a_i x^{b_i}$
Find the value of f(1) expressed in terms of $b_1, b_2, ..., b_n$ and $n$.

# A cute geometry problem

Given a square $ABCD$, and a point $P$ inside it, such that $PA=4, PB=7$ and $PC=9$.

Find $\angle APB$.