[ $[$ Divisibility rules for 3 and 9$]$

The teacher wrote two natural numbers on the board. Lёnya multiplied the first number by the sum of the digits of the second and got 201320132013. Fedia multiplied the second number by the sum of the digits of the first and got 201420142014. Did anyone of the boys make a mistake?

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Both products that the boys were supposed to calculate are divisible by 9 if and only if the product of the numbers written by the teacher is divisible by 9. However, the sum of the digits of the number 201320132013 is 18 (which means it is divisible by 9), while the sum of the digits of the number 201420142014 is 21 (which means it is not divisible by 9).

Thus, the boys could not have been right at the same time.

## Answer

One of them was wrong.