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# No. Properties

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Senior Manager
Joined: 05 Oct 2008
Posts: 267

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27 Jan 2009, 02:06
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Attachment:

PS_NoProp_E.JPG [ 50.01 KiB | Viewed 842 times ]
Manager
Joined: 27 Apr 2008
Posts: 110

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27 Jan 2009, 04:26
E

h(100)+1= 2^50*(1*2*3...50)+1, so all integers between 1 and 50 are factors of [2^50*(1*2*3...*50)], in which case they can not be factors of [2^50*(1*2*3...*50)+1].

thus, the smallest prime factor must be above 50--> E
Intern
Joined: 19 Jan 2009
Posts: 17

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27 Jan 2009, 07:08
Given h(100) = 2 x 4 x 6 x 8 ..........100
= 2(1) x 2(2) x 2 (3) x 2 (4) ........2(50)
= 2^50 x 1 x2 x 3 x4 ........50
Which implies h(100) is divisible by all numbers till 50

h(100) + 1 cannot be divisible by numbers till 50 ..as they would leave a remainder 1.
so the smallest prime factor of h(100) + 1 has to be greater than 50 .

SVP
Joined: 29 Aug 2007
Posts: 2467

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27 Jan 2009, 16:58
study wrote:
Attachment:
PS_NoProp_E.JPG

Detail work-out: 7-p556064?t=74417&hilit=smallest+prime#p556064
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Re: No. Properties   [#permalink] 27 Jan 2009, 16:58
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# No. Properties

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