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# Prime factor questions

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Intern
Joined: 27 Jul 2007
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27 Jul 2007, 13:09
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Hey all, i am having difficulty getting a hang of the prime factor questions. would be very glad if someone could show me the thought process to solve the following question:

What is the greatest prime factor of 4^17 - 2^28 ?
- 2
- 3
- 5
- 7
- 11

Also, although not as important:
Why is, if x<0, sqrt(-x|x|) = -x?
Is the sqrt of -4 equal to -2?

Many thanks for your help, Max
Director
Joined: 26 Feb 2006
Posts: 901
Followers: 4

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27 Jul 2007, 13:17
MaxCR1 wrote:
Hey all, i am having difficulty getting a hang of the prime factor questions. would be very glad if someone could show me the thought process to solve the following question:

What is the greatest prime factor of 4^17 - 2^28 ?
- 2
- 3
- 5
- 7
- 11

= 4^17 - 2^28
= 2^34 - 2^28
= 2^28 (2^6 -1)
= 2^28 (63)

now it should be 7.
Director
Joined: 26 Feb 2006
Posts: 901
Followers: 4

Kudos [?]: 123 [0], given: 0

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27 Jul 2007, 13:19
MaxCR1 wrote:
Why is, if x<0, sqrt(-x|x|) = -x?. Is the sqrt of -4 equal to -2?

sqrt of -4 is not equal to -2 but (-sqrt of 4) is equal to -2.
Intern
Joined: 27 Jul 2007
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 0

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27 Jul 2007, 13:49
many thanks for your promp help, i haven't done maths in quite a while..
i understand it to this part:
= 2^34 - 2^28

but i am unsure of the logic of substracting 1 from the 2^6:
= 2^28 (2^6 -1)
= 2^28 (63)

Is the formula:
a^b - a^c = a^c*[a^(a-c)-1]

What would it be for
a^b + a^c ?

Director
Joined: 26 Feb 2006
Posts: 901
Followers: 4

Kudos [?]: 123 [0], given: 0

### Show Tags

27 Jul 2007, 14:10
MaxCR1 wrote:
many thanks for your promp help, i haven't done maths in quite a while..
i understand it to this part:
= 2^34 - 2^28

but i am unsure of the logic of substracting 1 from the 2^6:
= 2^28 (2^6 -1)
= 2^28 (63)

Is the formula:
a^b - a^c = a^c*[a^(a-c)-1]

What would it be for
a^b + a^c ?

a^b - a^c = a^c [a^(b-c) - 1] for b>c
a^b + a^c = a^c (a^(b-c) + 1) for b>c
27 Jul 2007, 14:10
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