Problem:
Let . What is the ratio of the sum of the odd divisors of to the sum of the even divisors of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Answer (C): Let be the sum of the odd divisors of . The greatest power of 2 that divides is . Odd divisors of multiplied by 2,4 , and 8 yield all the even divisors of . Therefore the sum of the even divisors of is , and the requested ratio is .
The problems on this page are the property of the MAA's American Mathematics Competitions