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Omni-MATH / Determine whether or not there exist two different sets A,B, each consisting of at most 2011² positive integers, such that every x with 0<x<1 satisfies the following inequality: …

Problem

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problem

Determine whether or not there exist two different sets

A,B

, each consisting of at most

2011^2

positive integers, such that every

x

with

0 < x < 1

satisfies the following inequality:

\left| \sum_{a \in A} x^a - \sum_{b \in B} x^b \right| < (1-x)^{2011}.

Plain-text mathematical notation (without MathML)

Determine whether or not there exist two different sets A,B, each consisting of at most 2011² positive integers, such that every x with 0<x<1 satisfies the following inequality:
|∑_(a∈A)x^(a)−∑_(b∈B)x^(b)|<(1−x)²⁰¹¹.

Original LaTeX notation

Determine whether or not there exist two different sets $A,B$, each consisting of at most $2011^2$ positive integers, such that every $x$ with $0 < x < 1$ satisfies the following inequality:
\[\left| \sum_{a \in A} x^a - \sum_{b \in B} x^b \right| < (1-x)^{2011}.\]

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task_id: a608ae72-f75e-5c87-8c60-16e6769b5dfa
task_key: test--a608ae72-f75e-5c87-8c60-16e6769b5dfa
task_revision_id: 4
config / split: / test

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