Let A be a positive integer. Let D(A) be the number of solutions of xyz=A where x, y, and z are all positive integers; thus, D(6)=9. Let d(A) be the number of positive divisors of A, so d(6)=4.
Show that d(A)²-2D(A)+d(A)≥0. When does the equality hold?
(In reply to
re(2): solution with proof (quick fix) by Daniel)
Very nice Solution. I guess the statement d(A)+1≥2v needs to be
proved by Mathematical Induction. The solution I am going to submit
follows a very different approach.
Edited on August 14, 2007, 2:53 am
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Posted by Praneeth
on 2007-08-14 02:51:47 |
re: solution with proof (quick fix)
