数学题一道请教高人

jiyiflora

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

    

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

    

a.   
between 20 and 10

    

b.   
between 10 and 20

    

c.   
between 20 and 30

    

d.   
between 30 and 40

    

e.   
greater than 40

    Right Answer: E

carolssnz

网上google了一下，供参考。

this is definitely a difficult number properties question. Let's first consider the prime factors of h(100). According to the given function,
h(100) = 2*4*6*8*...*100

By factoring a 2 from each term of our function, h(100) can be rewritten as
2^50*(1*2*3*...*50).

Thus, all integers up to 50 - including all prime numbers up to 50 - are factors of h(100).

Therefore, h(100) + 1
        cannot have any prime factors 50 or below, since dividing this value by any of these prime numbers will yield a remainder of 1.

Since the smallest prime number that can be a factor of h(100) + 1 has to be greater than 50, The correct answer is E.

JUDYLI

谢谢LS的，我也正想知道这题。

sysxy1987

多谢分享，正好想知道！

yjz809

just wanna add something, 50 is not a prim number, but 47 is. The smallest prime number, therefore, has to be greater than 47, rather than 50