24) The number 100020001 is:
(A) a prime number,
(D) a perfect cube,
(B) a perfect square, (C) a multiple of three,
(E) a multiple of eleven.

![](https://cdn.mathpix.com/cropped/2024_04_17_84f5f6e83b5066604abfg-2.jpg?height=343&width=354&top_left_y=507&top_left_x=2419)
24. The answer is $\mathbf{( B )}$.

Using the well-known divisibility criteria for 3 and 11, we can immediately exclude answers $\mathbf{C}$ and E. Then, recalling the formula for the square of a binomial, we have that $(10000+1)^{2}=$ $100000000+2 \cdot 10000+1=100020001$, which means the given number is a perfect square (so $\mathbf{A}$ is also false). If $\mathbf{D}$ were also true, the given number would have to be both a cube and a square of an integer, i.e., it would have to be the sixth power of an integer. In other words, 10001 would have to be a cube of an integer, but this is not the case. The only possible answer is $\mathbf{B}$.