Five. (Full marks 15 points) There are 1998 athletes with numbers from 1 to 1998. Select some of these athletes to participate in the honor guard, but ensure that among the remaining athletes, no one's number is equal to the product of the numbers of any two other athletes. How many athletes can be selected for the honor guard at a minimum? Provide your selection plan and briefly explain your reasoning.

---

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
Five, the selectable numbers are $2,3,4, \cdots, 43,44$, these 43 athletes can be chosen as flag bearers to meet the requirements of the problem. The reason is as follows:

After selecting these 43 athletes as flag bearers, the product of any two numbers among the remaining athletes' numbers (excluding number 1) will be greater than $45^{2}=2025>1998$. And 1 multiplied by any number will not equal a third different number. Therefore, among the remaining athletes, there is no one whose number is equal to the product of the numbers of two other athletes.

Now we prove that 43 is the minimum number of athletes that can be selected as flag bearers. That is, we need to prove that when 42 athletes are selected as flag bearers, there will be at least three numbers among the remaining athletes, where the product of two of these numbers equals the third number. For this, we examine the triplets:

Since the function $x(89-x)$ is increasing in the interval $2 \leqslant x \leqslant 44$, the numbers written are distinct and do not exceed $44 \times 45=1980<1998$. There are 43 such triplets. If the number of selected athletes is less than 43, at most 42, at least one of these 43 triplets will have all three numbers unselected. Then these three numbers, as the numbers of the remaining athletes, will have one number equal to the product of the other two, which does not meet the problem's requirements. Therefore, the number of athletes selected as flag bearers must be at least 43.
(Supplied by Zhou Chunli, Department of Mathematics, Capital Normal University)