请教PP1-PS的题目算法??

All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet.  Which of the following gives the maximum number of different stocks that can be designated with these codes?

答案是:c...不了解~~

(A) 2(26^5)

(B) 26(26^4)

(C) 27(26^4)

(D) 26(26^5)

(E) 27(26^5)

还有一题:

For every positive even interger n, the function h(n) is defined to be the product of all the interger from 2 to n, inclusive. 

If p is the smallest prime factor of h(100)+1, then p is

答案是: greater than 40..请问该怎么算呢? 

请大大们指点~~感谢

26^4+26^5=27*26^4

refer to this link:

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http://forum.chasedream.com/dispbbs.asp?BoardID=22&replyID=1733108&id=183630&skin=0

All the stocks are designated by a 4 or 5letter code, it is like:abcd,or abcde,....zasde.....blablabla....

for a stock that is designated by a 4letter code, the amount is 26*26*26*26=26^4

as for a stocke that is designated by a 5 letter code, the amount is 26*26*26*26*26=26^5=26*26^4

add these two together, the answer is 27*26^4

1) The maximum number possible is when both the set can be repeated numbers.

So 26^4 + 26^5 = 27 (26^4)

2) Should be problem say "even integers from 2 to n"?

refer to this link:

please search first

http://forum.chasedream.com/dispbbs.asp?BoardID=22&replyID=1733108&id=183630&skin=0

as for the 2nd question, you have to be aware that

for 2 consecutive number, such as h(100) and h(100)+1, there is no common prime number

so a prime number for h(100) is definitly not one for h(100)+1

h(100)=2*4*6*...*100
两个数互质说明除1以外没共同因子。因为2-50是h(100)的因子，所以不是h(100)+1的因子。

而2到50中最大的质数是47。

所以h(100)+1的质因子必然大于47。