Diophantine triples with values in the sequences of Fibonacci and Lucas numbers

Sa？etak Let FL={1,2,3,4,5,7,8,11,13,18,21, … } be the set consisting of all Fibonacci and Lucas numbers with positive subscripts. We find all triples (a,b,c) of positive integers a < b < c such that ab+1, ac+1, bc+1 are all members of FL