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Could you help me, please, to Compute the number of different ways there are to put jewels of $k$ different kinds on a crown with $p$ identical places for jewels, with $p$ a prime?

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    In the question is not specified but I think that we have an inexhaustible supply and the crown is circular2011-11-26
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    Make a little scratch on the crown just above a place for a jewel. Then there are $k^p$ ways to place the jewels on the scratched crown, including $k$ where the $p$ jewels are identical. Forget temporarily about those, and think of the remaining $k^p-k$. Now cover the scratch and rotate the crown.2011-11-26
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    Please include these details in your question so that others do not have to read deep into the comments to understand it.2011-11-26
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    @Austin Mohr: Crowns have spiky things on top, and must be quite uncomfortable worn upside down. Is there a King or Queen on Stack Exchange who can clarify things?2011-11-26
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    @AndréNicolas I suppose what I was thinking of is properly called a circlet: http://www.wulflund.com/images_items/medieval-gothic-circlet---brass-obsidian_3.jpg2011-11-26
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    @AndréNicolas: True for most crowns, but not always: e.g., [the Iron Crown of Lombardy](http://en.wikipedia.org/wiki/Iron_Crown_of_Lombardy).2011-11-26

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