Tribonacci序列与丢番图数组OA

This paper studies a variant of the Diophantine tuples problem,namely,finding triples of Jacobsthal-Lucas numbers such that the product of any two plus one is a Tribonacci number.The problem can be transformed into a Diophantine equation.By using Binet formulas,the equation is rewritten in some linear forms in logarithms,an upper bound for the solutions is obtained by applying Matveev′s theorem,then a reduction method is used to reduce this bound to a computationally feasible range.Finally,with the aid of computer search,it is found that no triple satisfies the required conditions.