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Omni-MATH / In how many ways can the set of ordered pairs of integers be colored red and…

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problem

In how many ways can the set of ordered pairs of integers be colored red and blue such that for all aa and bb, the points (a,b),(−1−b,a+1)(a, b),(-1-b, a+1), and (1−b,a−1)(1-b, a-1) are all the same color?
Plain-text mathematical notation (without MathML)
In how many ways can the set of ordered pairs of integers be colored red and blue such that for all a and b, the points (a,b),(−1−b,a+1), and (1−b,a−1) are all the same color?
Original LaTeX notation
In how many ways can the set of ordered pairs of integers be colored red and blue such that for all $a$ and $b$, the points $(a, b),(-1-b, a+1)$, and $(1-b, a-1)$ are all the same color?

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