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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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sirm3dBest ResponseYou've already chosen the best response.0
\[\Huge h(n)=2^{n/2} \cdot (n/2)!\] the smallest prime number that is not a repeat is 29.
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.1
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
 one year ago

sirm3dBest ResponseYou've already chosen the best response.0
ah, h(100) + 1. i missed that +1
 one year ago

matrickedBest ResponseYou've already chosen the best response.0
though for that part u r absolutely correct
 one year ago
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