A note on the number of D(4)-quintuples

Sa？etak In this paper we will significantly improve the known bound on the number of D(4)-quintuples, illustrating the elegant use of the results the authors proved in [1] together with more efficient way of counting the number of m-tuples that was introduced in [5]. More precisely, we prove that there are at most 7 · 10^36 D(4)-quintuples