On the shifted product of binary recurrences - Khadir O (JOURNAL OF INTEGER SEQUENCES - ONLINE, 2010)
The present paper studies the diophantine equation GnHn + c = x2n and related questions, where the integer binary recurrence sequences G, H and {x} satisfy the same recurrence relation, and c is a given integer. We prove necessary and sufficient conditions for the solubility of GnHn + c = x2n. Finally, a few relevant examples are provided.