Friday, November 13, 2009

Liouville Problem-Two Column Approach


I forgot to do the case for 1
So 1 has 1 factor, that is 1
so the sum of the number of factors squared is 1.
Sum of the cubes of the factors of 1 is 1.
So that is the 1 = 1. The sum of cubes of the factors then becomes larger than the sum of the number of factors of the factors as you go higher one.


Thoughts: Well if I was a high school student, I would be happy with such findings. We were like are we supposed to prove it or?
I figured Stan will have some nice elegant proof.

2 comments:

  1. Woops I read this question over and over again. I think I did this problem wrong the second time. I thought I was doing the sum of the (cubes of the divisors). Eek!

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  2. Well, technically your conjecture seems to hold true except for the situation of the prime number 1, where you get 1=1. You seemed to have a logical progression, starting with prime numbers and increasing the number of divisors. Looks like everyone in our group came to a different conclusion. Good job two-columning that problem!

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