Kovaldjei A.K.

A student did not notice the multiplication sign between two three-digit numbers and wrote a single six-digit number. The result turned out to be three times larger.

Find these numbers.
Let $A$ be the first three-digit number, and $B$ be the second. According to the condition, $1000 A + B = 3 A B$, from which $(3 A - 1) B = 1000 A$.

The numbers $A$ and $3 A - 1$ are coprime, so 1000 must be divisible by $3 A - 1$. Since $A$ is a three-digit number, $3 A - 1$ is a three-digit or four-digit number. There are two such divisors of 1000: 500 and 1000. $3 A - 1$ cannot equal 1000, because 1001 is not divisible by 3. Therefore, $3 A - 1 = 500$, from which $A = 167, B = 334$.

## Answer

167 and 334.