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Let d be the sum of the lengths of all the diagonals of a plane convex polygon with n vertices (where n>3). Let p be its perimeter. Prove that:
n-3<{2d\over p}<\Bigl[{n\over2}\Bigr]\cdot\Bigl[{n+1\over 2}\Bigr]-2,
where [x] denotes the greatest integer not exceeding x.

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