Task 1. Write the number 100000 as a product of two numbers whose representations contain no digit 0.
Solution. We have $100000=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5$. The number 100000 needs to be written as a product of two numbers whose representations do not contain the digit 0, so we get that in neither of the factors the numbers 2 and 5 should be together. According to this, the solution to the problem is:

$$
100000=(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2) \cdot(5 \cdot 5 \cdot 5 \cdot 5 \cdot 5)=32 \cdot 3125
$$