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**tony123****Member**- Registered: 2007-08-03
- Posts: 189

For how many positive integers n is

an integer ?

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

If *n* is a positive even integer,

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 integerThen

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 integersSo there are only three positive integers *n* (namely

is an integer.

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**tony123****Member**- Registered: 2007-08-03
- Posts: 189

Very nice work Jane thank you

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