## Posts

Showing posts from August, 2022

### 2006 IMO #G3

Let $ABCDE$ be a convex pentagon such that $\angle BAC = \angle CAD = \angle DAE\qquad \text{and}\qquad \angle ABC = \angle ACD = \angle ADE.$The diagonals $BD$ and $CE$ meet at $P$. Prove that the line $AP$ bisects the side $CD$.

### Problem request: 2022 AIME II #13

Hi everyone,  I hope you had a great summer!  I was not posting for about a month or so because not many people were viewing the blog in the summer.  I'm going to start to post frequently again, and for now I have a problem request I got a couple days ago.  There is a polynomial $P(x)$ with integer coefficients such that$P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}$holds for every $0<x<1.$ Find the coefficient of $x^{2022}$ in $P(x)$.