## Task 2 - 330612

Two numbers should have a sum of 2028. If the first number is divided by 28, the result should be the same as when the second number is divided by 128.

Show that the two numbers are uniquely determined by these conditions; find them and confirm that they meet the conditions!
If $d$ is the result of dividing the first number by 28, then the first number is 28 . $d$. Since $d$ is also the result of dividing the second number by 128, the second number is 128 . $d$. Consequently, the sum of the two numbers $28 \cdot d$ and $128 \cdot d$ is $156 \cdot d$; thus, $156 \cdot d = 2028$ must hold.

From this, it follows that $d = 2028$ : $156 = 13$. Therefore, the first and second numbers are uniquely determined as $28 \cdot 13 = 364$ and 128 . $13 = 1664$, respectively.

For these, one can verify: 364 : 28 and 1664 : 128 yield the same result 13, and $364 + 1664 = 2028$ holds.