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 January 3rd, 2016, 03:07 PM #1 Newbie   Joined: Jan 2016 From: Croatia Posts: 2 Thanks: 0 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.
 January 3rd, 2016, 04:43 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 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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