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Omni-MATH / An integer n>1 is given . Find the smallest positive number m satisfying the following conditions： for any set {a,b} ⊂{1,2,⋯,2n−1} ,there are non-negative integers x,y ( not all ze…

Problem

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problem

An integer

n>1

is given . Find the smallest positive number

m

satisfying the following conditions： for any set

\{a,b\}

\subset \{1,2,\cdots,2n-1\}

,there are non-negative integers

x, y

( not all zero) such that

2n|ax+by

and

x+y\leq m.

Plain-text mathematical notation (without MathML)

An integer  n>1 is given .  Find the smallest positive number m satisfying the following conditions： for any set {a,b} ⊂{1,2,⋯,2n−1} ,there are non-negative integers   x,y  ( not all zero)  such  that   2n|ax+by and x+y≤m.

Original LaTeX notation

An integer  $n>1$ is given .  Find the smallest positive number $m$ satisfying the following conditions： for any set $\{a,b\}$ $\subset \{1,2,\cdots,2n-1\}$ ,there are non-negative integers   $ x, y$  ( not all zero)  such  that   $2n|ax+by$ and $x+y\leq m.$

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task_id: f56bc5a8-4c0a-5cb0-8da2-d9b88e676276
task_key: test--f56bc5a8-4c0a-5cb0-8da2-d9b88e676276
task_revision_id: 4
config / split: / test

Official source

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