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January 3rd, 2016, 03:07 PM   #1
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Need help

The number of all even divisers of some natural number is 3 more than the number of all odd divisers.What is the ratio of the sum of all the even-numbered divisors and the sum of all its odd divisors? Find all possibly answers.
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January 3rd, 2016, 04:43 PM   #2
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This is a good problem!

Let $n$ be the number we're looking at.

Write a general prime factorisation of $n$ (What prime factor do you know $n$ has?).
Write out the number of odd divisors of $n$ using the prime factorisation.
Write out the number of even divisors of $n$ using the prime factorisation.
How do they relate?
After that, there's a little bit of casework and the answer falls out.
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