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October 3rd, 2013, 03:52 PM   #1
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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



and

.

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?
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October 9th, 2013, 01:46 PM   #2
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Re: A Few Interesting Problems

For question 3, what field are the entries in A from?
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October 9th, 2013, 03:16 PM   #3
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Re: A Few Interesting Problems

Actually, they all have to be positive integers.
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