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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. smile


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#3 2008-11-10 06:27:48

tony123
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Re: how many positive integers

Very nice work Jane thank you

 

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