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.

IF A = 1/2*(15+V197)  LET B=1/2*(15-V197)

A*B=1/4*28=7

A^n*B^n=7^n

    I ERASED THE ERRONEOUS SEQUEL

WILL TRY FOR ANOTHER SOLUTION

HOW ABOUT A HINT??

 

Edited on February 26, 2007, 8:14 am

Posted by Ady TZIDON on 2007-02-25 16:23:23