many days of the year can be Adel’s birthday?
Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E6
May 25, 2024
number theory
Problem Statement
In Eldorado a year has months, and each month has days. One day Brigi asked Adél who lives in Eldorado what day her birthday is. Adél answered that she is only going to tell her the product of the month and the day in her birthday. (For example, if she was born on the th day of the th month, she would say .) From this, Brigi was able to tell Adél’s birthday. Based on this information, how many days of the year can be Adél’s birthday?