2. On the eve of his birthday in 2015, Dima discovered an amazing fact: if you multiply the number (day of the month) of his birth by the month number of his birth and by the number of years he is turning, you get the year of his birth. Dima was born in the 21st century. Determine all possible dates of his birth.

Answer: July 22, 2002 or November 14, 2002.

Solution. Let Dima be $x$ years old in 2015. Denote the day of the month of his birth by $d$ and the month number by $m$. From the problem statement, we get the following equation: $(d \cdot m + 1) \cdot x = 2015 = 5 \cdot 13 \cdot 31$. Dima is less than 15 years old (since he was born in the 21st century) and more than 5 (since the product of the day of the month and the month number of his birth is no more than

$31 \cdot 12 = 372$). Therefore, Dima is 13 years old this year and he was born in 2002. Then $d \cdot m = 154 = 2 \cdot 7 \cdot 11$. From this, we get two options corresponding to the day and month of his birth: $154 = 14 \cdot 11$, i.e., November 14, and $154 = 22 \cdot 7$, i.e., July 22.

Criteria for evaluation.

One answer is missing - 4 points.
Brute force solution by iterating through years and incomplete iteration - no more than 3 points.


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