Question

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 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40

Answer 1

\[\Huge h(n)=2^{n/2} \cdot (n/2)!\]
the smallest prime number that is not a repeat is 29.

Answer 2

h(100) = 2*4*6...100
if you observe properly, it is written (2^50)*(1*2..50) or (2^50)*(50 !)

we are concerned about (2^50)*(50!) +1

note that h(100) and h(100) +1 are both consecutive nos. , thus they dont share ANY common factor apart from 1 .
h(100) clearly has all prime factors from 1 to 50 as its factors, thus h(100)+1 cant have those as factors.
hence ans would be greater than 50 according to me, or E

Answer 3

ah, h(100) + 1. i missed that +1

Answer 4

though for that part u r absolutely correct