Contructions of some new nonextandable P_k sets
K. Kaygisiz, H. Senay · International Mathematical Forum · 2007
Let k be an integer, A is a set {x1, x2, x3,...xn} with n positive different integers. A set is called Pk, if i, j ∈ N and i = j, xixj + k is a square of an integer. In our research we studied on set Pk.We proved that sets P7 = {1, 2, 9}, P−7 = {1, 8, 11, 16} and P−7 = {2, 4, 8} can not be extended. In addition, we showed that there is no P−7 set that contains any multiple of 3 or 5. Furthermore it is proven that sets Pk, {k = 4t+ 2, k = 4t+ 3, t ∈ Z} can contain at most 1 even number as an element.