The simultaneous diophantine equations У2-5x2=4 and z2-442x2=441

الملخص EN

The three numbers 1, 5, and 442 have the property that the product of any two numbers decreased by 1 is a perfect square.

In this paper it is proved that there is no other positive integer which shares this property with 1, 5, and 442.

Mathematics Subject Classification: Primary 11D09, 11D25, Secondary 11B37, 11J68, 11J86, 11Y50.