Let denote the number of positive divisors of the positive integer , and the sum of the positive divisors of . Show that
Last edited by Bruno J.; May 18th 2010 at 03:17 PM.
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Originally Posted by Bruno J. Let denote the number of positive divisors of the positive integer , and the sum of the positive divisors of . Show that we also need to have recall that for any distinct (real) numbers we have thus: to prove the other inequality first note that since we have and so using this we have:
Great job! (Thanks for specifying ). Here's how I proved the first inequality; we have , and by the arithmetic/geometric mean inequality.
Originally Posted by Bruno J. Here's how I proved the first inequality; we have , and by the arithmetic/geometric mean inequality. oh yeah, this is easier!
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