Problem:
Anh read a book. On the first day she read pages in minutes, where and are positive integers. On the second day Anh read pages in minutes. Each day thereafter Anh read one more page than she read on the previous day, and it took her one more minute than on the previous day until she completely read the page book. It took her a total of minutes to read the book. Find .
Solution:
Let represent the number of days it took Anh to finish the book. Then the total number pages read is , and the total number of minutes taken is . Thus and . Note also that . Then must be a common factor of and so must be a factor of . Because , it follows that . Then and . Therefore and . The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions