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Divisible by 7 (Posted on 2007-02-15) Difficulty: 3 of 5
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.

See The Solution Submitted by Dennis    
Rating: 4.0000 (1 votes)

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Solution LOOK 4 THE CONJUGATE | Comment 1 of 5

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

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