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## HMMT 2015 Algebra #3 본문

HMMT/2015

### HMMT 2015 Algebra #3

수악중독 2015.03.15 08:39

Let P be a real number and $c \ne 0$ an integer such that$c-0.1 < x^p \left ( \dfrac{1-(1+x)^10}{1+(1+x)^10} \right ) < c+0.1$ for all (positive) real numbers $x$ with $0<x<10^{-100}$. (The exact value $10^{-100}$ is not important. You could replace it with any "sufficiently small number".) Find the ordered pair $(p, \;c)$.

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