Arkin, Joseph; Bergum, Gerald More on the problem of Diophantus. (English) Zbl 0649.10011 Applications of Fibonacci numbers, Proc. 2nd Int. Conf., San Jose/Cal., August 1986, 177-181 (1988). A number of recent papers have dealt with the problem of finding a set of four numbers with the property that the product of any two distinct elements of the set when increased by a specified integer is a square. In the present paper several solutions of this problem are given. Most of the paper, however, is devoted to finding a set of five rational numbers, not all of which are integers, such that the product of any two is one less than the square of a rational number.[For the entire collection see Zbl 0635.00004.] Reviewer: Peter Hagis jun. (Philadelphia) MSC: 11D99 Diophantine equations Keywords:rational analogue; diophantine quadruple; quintuple Citations:Zbl 0635.00004 PDFBibTeX XML