4. Find the number which, when divided by 143, gives a remainder of 132, and when divided by 144, gives the same quotient and a remainder of 108.
Solution. The desired number is of the form $a=143b+132$ and $a=144b+108$. Therefore, $143b+132=144b+108$, from which it follows that $b=24$. The desired number is $a=143 \cdot 24+132=3564$.

## VI section