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Math question - not homework?
For every positive integer n, h(n) is a product of even integers from 2 to n. If p is the smallest prime factor of h(100) +1, what is p?
a) 2<p<10
b) 10<p<20
c) 20 <p<30
d) 30<p<40
e) 40<p
I care more about the method for getting it done than the answer. Any help?
1 Answer
- Anonymous1 decade agoFavorite Answer
From your definition of h(n),
h(n) = 2 * 4 * 6 * 8 *... * n
h(n) = 2^n (1 * 2 * 3 * ... * (n/2))
h(n) = 2^n (n/2)!
h(100) = 2^100 (50)!
This means that every number from 2 to 50 is a factor of h(100), which means that none of the numbers from 2 to 50 are factors of h(100) + 1. The smallest prime factor of h(100) + 1 has to be bigger than 50. Your answer is e.