... Mathematics, 163 (2006), 969–1018 Classical and modular approaches to exponential Diophantine equations I Fibonacci and Lucas perfect powers By Yann Bugeaud, Maurice Mignotte, and Samir Siksek* Abstract ... combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, and 144 and the only perfect powers in the Lucas sequence are and Introduction ... problem A sequel combining the classical and modular approaches for Diophantine equations of the form x2 + D = y p has just been completed [13] CLASSICAL AND MODULAR APPROACHES 971 We delay presenting...