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.