Finite Differences

by First, Dec 3, 2016, 10:36 PM

2016 AIME #11 wrote:

Let $P(x)$ be a nonzero polynomial such that $(x-1)P(x+1)=(x+2)P(x)$ for every real $x$ , and $\left(P(2)\right)^2 = P(3)$ . Then $P\left(\frac{7}{2}\right)=\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .

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There was an almost identical problem in 108 (which I unfortunately saw after seeing this problem for the first time)

...rip MAA

by shiningsunnyday, Dec 4, 2016, 1:07 AM

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Didn't you take the 2016 AIME II? Also is 108 just problems or topics covered and examples presented?

by First, Dec 4, 2016, 2:02 AM

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Let $ABC$ be an equilateral triangle of side length $1$ . Let $D$ be the point such that $C$ is the midpoint of $BD$ , and let $I$ be the incenter of triangle $ACD$ . Let $E$ be the point on line $AB$ such that $DE$ and $BI$ are perpendicular. $ \
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Problems of the day

Finite Differences

by First, Dec 3, 2016, 10:36 PM

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