求助 一数学题 谢谢

dpzixuan89

h(n)=2*4*6*8*10*...........*n
p是the smallest prime factor of h(100)+1
求p的范围
A 2-10
B 10-20
C 20-30
D 30-40
E greater than 40

dpzixuan89

是PREP上的题。。每次做都遇到。。谁能告诉我方法？？？？

eflet222

Guest, 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.

Hope that helps
-Dan

dpzixuan89

懂了。。谢谢