TITLE: Can two sets have same AM, GM, HM?
QUESTION [5 upvotes]: Can two set of numbers(same size) have same arithmetic , geometric, and harmonic mean ?
When I say different set they must differ by at-least $1$ element and also what if set is not be of distinct elements?

REPLY [6 votes]: Yes. In fact, you can find solutions in the integers.
$\{-4, -3, 1, 3, 4\}$
$\{-6, -2, 1, 2, 6\}$