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# Distinct factors

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Distinct factors [#permalink]  08 Feb 2004, 07:43
The answer is B. However if n = 110, the two positive factors are 11 x 10, and the difference is odd. So, n need not be 2. Can anyone enlighten?

243.
If the integer n is greater than 1, is n equal to 2?

1. n has exactly two positive factors.
2. The difference of any two distinct positive factors of n is odd.
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Please dont post the answer. Everyone will be at loss including you. Even if few get the wrong answer it will still be interesting to go through their logic. You will learn a lot. If post answers then those who get it wrong will never post.

A) if N has two distinct +ve factors then N is prime number.
Prime numbers are 2, 3, 5 .... So we dont know if n>=2
B) Difference between any two distinct +ve factors is odd
4 has factors as 1,2 and 4
4-1 = 3 4-2 = 2 so 4 cannot be it.
All even numbers except 2 have more than 2 factors and the difference between any factors may or may not be even
One more Ex N = 6 which as 1,2,3 and 6 as factors. 6-2 = 4 which even
and 6-3 = 3 which odd
Take any prime number. Since prime N is always odd and has only two distinct +ve factors N and 1 N-1 is always even. Except for 2

This rule holds good for only 2.

So B is sufficeint.

110 has 11,10,5 and 2 as factors
11-10 = 1 odd
10-2 = 8 even.
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