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22 Dec 2009, 11:23
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22 Dec 2009, 12:15
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It's (E) - greater than 40. I'll try to explain:
H(100) = 2*4*6*8*. . .*100 = (1*2*3*4*5* . . . *50)*2^50
It's easy to see from here that H(100) is multiple of each and every integer from 1 to 50 inclusive. And H(100) + 1 can not possibly be divided by these integers. So, if H(100) + 1 has some prime factor, then smallest of them can't be less than 40
Please correct me if I'm wrong.
H(100) = 2*4*6*8*. . .*100 = (1*2*3*4*5* . . . *50)*2^50
It's easy to see from here that H(100) is multiple of each and every integer from 1 to 50 inclusive. And H(100) + 1 can not possibly be divided by these integers. So, if H(100) + 1 has some prime factor, then smallest of them can't be less than 40
Please correct me if I'm wrong.
22 Dec 2009, 12:23
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correct as E...
only point as mentioned h(100)+1 will not be divisible by any of int from 2 to 100.... h(100)+1 is itself a prime no... so smallest prime factor by which it will be divisible will be h(100)+1 itself
only point as mentioned h(100)+1 will not be divisible by any of int from 2 to 100.... h(100)+1 is itself a prime no... so smallest prime factor by which it will be divisible will be h(100)+1 itself
