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# What is the largest prime number of 4^(17) - 2^(28) ???

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Intern
Joined: 03 Mar 2007
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What is the largest prime number of 4^(17) - 2^(28) ??? [#permalink]

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21 Mar 2007, 13:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the largest prime number of 4^(17) - 2^(28) ???
Thanks guys

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SVP
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21 Mar 2007, 13:44
7 for me

4^(17) - 2^(28)
= 2^(34) - 2^(28)
= 2^(28) * (2^6 - 1)
= 2^(28) * (2^3 - 1) * (2^3 + 1)
= 2^(28) * (8 - 1) * (8 + 1)
= 2^(28) * (7) * (3 * 3)

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21 Mar 2007, 14:20
tlntd177 wrote:
What is the largest prime number of 4^(17) - 2^(28) ???
Thanks guys

is it prime factor?
If yes then is it 7?

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Senior Manager
Joined: 11 Feb 2007
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21 Mar 2007, 17:15
(4^17) - (2^28)

= [(2^2)^17] - (2^28)

= (2^34) - (2^28)

= 2^28[(2^6)-1]

= 2^28(64-1)

= 2^28(63)

63 = 7 x (3^2)

Therefore, 7.

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Intern
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21 Mar 2007, 22:21
Hey Guys thanks... I posted 2 more questions...
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2more questions.doc [115 KiB]

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2 more questions attached   [#permalink] 21 Mar 2007, 22:21
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# What is the largest prime number of 4^(17) - 2^(28) ???

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