A blog for enthusiastic math-lovers!

AMC 2012 problem

This month has been crazy! It’s almost February 29th, since 2012 is a leap year. About a month ago I attended SUMiT and had an amazing time. I met many people my age interested in math like me. It was organized very well, thanks to GirlAngle and others.

Also in the past month were the AMC’s. On the AMC12 A, there was one problem that particularly intrigued me problem 2: See if you find a nice solution

Consider the polynomial

P(x)=\prod_{k=0}^{10}(x^{2^k}+2^k)=(x+1)(x^2+2)(x^4+4)\cdots (x^{1024}+1024)

The coefficient of x^{2012} is equal to 2^a. What is a?

\textbf{(A)}\ 5\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 24


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