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## #1 2008-11-09 22:01:05

tony123
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### how many positive integers

For how many positive integers n is

an integer ?

## #2 2008-11-10 03:19:31

JaneFairfax
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### Re: how many positive integers

If 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.

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #3 2008-11-10 06:27:48

tony123
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### Re: how many positive integers

Very nice work Jane thank you