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Archive for May 4th, 2009

A37 If n is a natural number, prove that the number

(n + 1)(n + 2)\cdots(n + 10)

is not a perfect square.

A9 Prove that among any ten consecutive positive integers at least one is relatively prime to the product of the others.

O51 Prove the among 16 consecutive integers it is always possible to find one which is relatively prime to all the rest.

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