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Omni-MATH / Find the smallest integer n such that each subset of {1,2,…,2004} with n elements has two distinct elements a and b for which a²−b² is a multiple of 2004.

Problem

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problem

Find the smallest integer nn such that each subset of {1,2,…,2004}\{1,2,\ldots, 2004\} with nn elements has two distinct elements aa and bb for which a2−b2a^2-b^2 is a multiple of 20042004.
Plain-text mathematical notation (without MathML)
Find the smallest integer n such that each subset of {1,2,…,2004} with n elements has two distinct elements a and b for which a²−b² is a multiple of 2004.
Original LaTeX notation
Find the smallest integer $n$ such that each subset of $\{1,2,\ldots, 2004\}$ with $n$ elements has two distinct elements $a$ and $b$ for which $a^2-b^2$ is a multiple of $2004$.

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Source and history

task_id
d88d4826-9913-51bc-86ac-cfcb9fbc051d
task_key
test--d88d4826-9913-51bc-86ac-cfcb9fbc051d
task_revision_id
1
config / split
/ test

Official source

initial import