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Omni-MATH / For which positive integers n is there an n×n matrix with integer entries such that every dot product of a row with itself is even, while every dot product of two different rows is…

Problem

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problem

For which positive integers nn is there an n×nn \times n matrix with integer entries such that every dot product of a row with itself is even, while every dot product of two different rows is odd?
Plain-text mathematical notation (without MathML)
For which positive integers n is there an n×n matrix with integer entries such that every dot product of a row with itself is even, while every dot product of two different rows is odd?
Original LaTeX notation
For which positive integers $n$ is there an $n \times n$ matrix with integer entries such that every dot product of a row with itself is even, while every dot product of two different rows is odd?

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Source and history

task_id
3d50ece7-1178-574c-b904-628c5d26a90f
task_key
test--3d50ece7-1178-574c-b904-628c5d26a90f
task_revision_id
1
config / split
/ test

Official source

initial import