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Given polynomials f₁, , fₙ in m variables with integral coefficients, we give upper bounds for the number of integral m-tuples u₁, , uₙ of bounded height such that f₁ (u₁), , fₙ (uₙ) are multiplicatively dependent. We also prove, under certain conditions, a finiteness result for u Zᵐ with relatively prime entries such that f₁ (u), , fₙ (u) are multiplicatively dependent.
Marley Young (Wed,) studied this question.
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