Find solutions for $$^nP_r=s!$$
For $(n,r,s)\in \mathbb{N}$
I could find some trivial solutions
$(6,3,5)~,~(1,1,1)$ etc.
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Please explain why downvoted? – Hawk Dec 11 '13 at 09:56
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Please explain the notation $^nP_r$. – user37238 Dec 11 '13 at 10:02
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$\dfrac{n!}{(n-r)!}$ – Hawk Dec 11 '13 at 10:03
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This, this and this threads should help. – Raymond Manzoni Dec 11 '13 at 10:05
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@RaymondManzoni.Thanks, they helped! – Hawk Dec 11 '13 at 10:07
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Glad it helped. You may find references too in Richard Guy's book "Unsolved Problems in Number Theory" (the pdf available at the end at 'Download Sample pages 1' contains the part B23 at page $117$ of the book). – Raymond Manzoni Dec 11 '13 at 10:20