Prove that if A = ½(15+√197), then 7 is a factor of [A^n] for all positive integer values of n, where [w] denotes the greatest integer less than or equal to w.

I'm not sure I follow the last step of your proof Ady. The number [(7^n)/(B^n)] is not necessarily divisible by 7 just because 0<B^n<1. For example, if B=7/9, 7 is not a factor of [(7^n)/(B^n)]. 

Posted by Dennis on 2007-02-25 21:39:20