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 October 3rd, 2013, 03:52 PM #1 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 A Few Interesting Problems 1. What is the smallest degree of a non-constant polynomial f(x), such that all roots of f(x) are in the set {0,2,3}, and the derivative of f(x) is divisible by 8x^2-24x+7? 2. Let x, y, and z be positive real numbers such that $xyz=945$ and $x(y+1)+y(z+1)+z(x+1)=385$. What is the minimum possible value of z+(y/2)+(x/4)? 3. Let A be a 6x6 matrix such that A^k is the identity matrix for some positive integer k. The smallest k is called the order of A. What is the largest possible order of A? 4. What is the most number of non-parallel lines in 7 dimensional space such that the angle between any two of them is the same?
 October 9th, 2013, 01:46 PM #2 Senior Member   Joined: Feb 2012 Posts: 628 Thanks: 1 Re: A Few Interesting Problems For question 3, what field are the entries in A from?
 October 9th, 2013, 03:16 PM #3 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 Re: A Few Interesting Problems Actually, they all have to be positive integers.

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