Two Olympiad Problems
1) Show that 1! + 2! + 3! + ...+ n! is not the square of any integer for n>3 .
2)Prove that of all the triangles with a given area K , the equilateral triangle has the shortest perimeter .
Neither of these problems should be too problematic but their solutions are simple . If you have an elegant solution to these problems then please post them .
Good luck !
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