AMO-Bench 2025 Problem 27

Find the number of integer solutions to $x^2 + y^2 + z^2 + 3(xy + yz + zx) + 5(x + y + z) + 1 = 0.$

Dataset text AMO-Bench. Open licence.

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Infinitely many. \textit{(Note: any answer conveying ``infinite'' is accepted.)}

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