## Task 4 - 080524

Determine two natural numbers $a$ and $b$ that simultaneously satisfy the following two conditions:

(1) The difference $a-b$ of the two natural numbers is 3.

(2) The product of these two natural numbers is 180.
The number 180 can only be factored into two factors \(a\) and \(b\) (with natural numbers \(a, b\)) in the following ways:

\[
180 = 180 \cdot 1 = 90 \cdot 2 = 60 \cdot 3 = 45 \cdot 4 = 36 \cdot 5 = 30 \cdot 6 = 20 \cdot 9 = 18 \cdot 10 = 15 \cdot 12
\]

Here, because \(15 - 12 = 3\), the condition (1) is only satisfied for \(a = 15\) and \(b = 12\).

Solutions of the II. Round 1968 taken from [5]

### 2.10 IX. Olympiad 1969

### 2.10.1 I. Round 1969, Class 5