## Task 2 - 060622

We are looking for the set of all natural numbers $a$ that satisfy the following conditions:

(1) $100<a<1201$,

(2) $a$ is divisible by 3, 4, and 5,

(3) $a$ is not divisible by 8, 9, or 25,

(4) $a$ leaves a remainder when divided by 11 that is divisible by 2.
Due to (2), $a$ is divisible by 60. Therefore, $a=60 \cdot b$, where $b$ is an integer, and due to (1), it follows that $100<60b<1201$. Thus, $b$ must satisfy the condition $1<b<21$.

Due to (3), $b$ cannot be divisible by 2, 3, or 5, and due to (4), it also cannot be divisible by 11.

Based on the above considerations, the only possible values for the factor $b$ are 7, 13, 17, and 19. Therefore, the numbers to consider are 420, 780, 1020, and 1140, all of which satisfy (1), (2), and (3). Of these, only 420, 780, and 1020 satisfy condition (4).

420, 780, and 1020 are the sought-after numbers. There are no other natural numbers that simultaneously satisfy (1) to (4).