A Polynomial Variant of a Problem of Diophantus for Pure Powers
نویسندگان
چکیده
In this paper, we prove that there does not exist a set of 11 polynomials with coefficients in a field of characteristic 0 with the property that the product of any two distinct elements plus 1 is a perfect square. Moreover, we prove that there does not exist a set of 5 polynomials and the property that the product of any two distinct elements plus 1 is a perfect kth power with k ≥ 7. Combining these results, we get an absolute upper bound for the size of a set with the property that the product of any two elements plus 1 is a pure power. 2000 Mathematics Subject Classification: 11D99, 11C08, 05D10.
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