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how many positive integersFor how many positive integers n is an integer ? #2 20081110 03:19:31
Re: how many positive integersIf n is a positive even integer, , which is not divisible by . Now suppose n is a positive odd integer. When . , which is divisible by 2, 8 and 32, but not by 128. Suppose is divisible by by 2, 8 and 32 but not by 128 for some odd integer n. Then is also divisible by 2, 8 and 32 but not by 128. Hence, by induction, is divisible by 2, 8 and 32 but not by 128 for all positive odd integers n. So there are only three positive integers n (namely ) for which is an integer. 