Thread: Problem 29
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Old July 2nd, 2007, 10:33 AM
mathisfun1 mathisfun1 is offline
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#1) For \Pi _i (a_i-i) to be odd then each odd a_i must be subtracted by an even integer. Because n is odd, \{a_1, a_2, ..., a_n\} has one more odd than even integer. Similarly, \{1, 2, ..., n \} has one less even integer than odd integer. So we must pair at least 1 odd integer a_i with an odd integer i. Hence the product is even.

Last edited by mathisfun1; July 3rd, 2007 at 02:41 PM.