Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

Aleksander Grelak: On The Equation (x2 - 1 )(y2 - 1) = z2

Corollary. Let a > 1 be an arbitrary fixed integer. Then all solutions in integers y,z of the equation are given by the formulae z = h JD{(A

x + Jdb

x)' - U - VDB, )' ] where D is squarefree kernel of a

2 -1 = Db

2 and < A

x ,B

} > is the least positive integer solution of the Pell's equation A

2~DB

2 = 1. REFERENCE [1] R. L. Graham, On a Diophantine equation arsing in graph theory, Eur. J. Comb. 1(1980), 107—122. [2] K. Szymiczek, On some Diophantine equations connected with triangular numbers (in Polish), Zeszyty Naukowe WSP Katowice - Sekcja Mat No 4(1964), 17—22. Institute of Mathematics Departament of Algebra and Number Theory Pedagogical University of Zielona Góra Zielona Góra, Poland 94