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Omni-MATH / Determine if there exists a (three-variable) polynomial P(x,y,z) with integer coefficients satisfying the following property: a positive integer n is [i]not[/i] a perfect square if…

Problem

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problem

Determine if there exists a (three-variable) polynomial

P(x,y,z)

with integer coefficients satisfying the following property: a positive integer

n

is [i]not[/i] a perfect square if and only if there is a triple

(x,y,z)

of positive integers such that

P(x,y,z) = n

Plain-text mathematical notation (without MathML)

Determine if there exists a (three-variable) polynomial P(x,y,z) with integer coefficients satisfying the following property: a positive integer n is [i]not[/i] a perfect square if and only if there is a triple (x,y,z) of positive integers such that P(x,y,z)=n.

Original LaTeX notation

Determine if there exists a (three-variable) polynomial $P(x,y,z)$ with integer coefficients satisfying the following property: a positive integer $n$ is [i]not[/i] a perfect square if and only if there is a triple $(x,y,z)$ of positive integers such that $P(x,y,z) = n$.

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task_id: 75216258-f5bf-50d5-b064-c1cd49059df6
task_key: test--75216258-f5bf-50d5-b064-c1cd49059df6
task_revision_id: 3
config / split: / test

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