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Another 𝑆-unit variant of Diophantine tuples
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-16 , DOI: 10.1090/proc/15193 Clemens Fuchs , Sebastian Heintze
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-16 , DOI: 10.1090/proc/15193 Clemens Fuchs , Sebastian Heintze
Abstract:We show that there are only finitely many triples of integers 
such that the product of any two of them is the value of a given polynomial with integer coefficients evaluated at an 
-unit that is also a positive integer. The proof is based on a result of Corvaja and Zannier and thus is ultimately a consequence of the Schmidt subspace theorem.
中文翻译：
Diophantine元组的另一个unit-unit变体
摘要：我们证明整数只有有限的三元组，使得它们中任意两个的乘积是给定多项式的值，并且整数系数在-unit处也是正整数。该证明基于Corvaja和Zannier的结果，因此最终是Schmidt子空间定理的结果。
更新日期：2020-10-16
such that the product of any two of them is the value of a given polynomial with integer coefficients evaluated at an -unit that is also a positive integer. The proof is based on a result of Corvaja and Zannier and thus is ultimately a consequence of the Schmidt subspace theorem. 中文翻译：
Diophantine元组的另一个unit-unit变体
摘要：我们证明整数只有有限的三元组，使得它们中任意两个的乘积是给定多项式的值，并且整数系数在-unit处也是正整数。该证明基于Corvaja和Zannier的结果，因此最终是Schmidt子空间定理的结果。
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