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# If n = 3^8 - 2^8, which of the following is NOT a factor of

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Manager
Joined: 24 Sep 2018
Posts: 100
Location: India
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

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23 Jul 2019, 03:09
If n = 3^8 - 2^8, which of the following is NOT a factor of n?

(A) 97
(B) 65
(C) 35
(D) 13
(E) 5

65 is the answer
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Bijaya

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Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

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23 Jul 2019, 03:36
BijayKru wrote:
If n = 3^8 - 2^8, which of the following is NOT a factor of n?

(A) 97
(B) 65
(C) 35
(D) 13
(E) 5

65 is the answer

$$n = 3^8 - 2^8$$
$$= (3^4 + 2^4)*(3^4 - 2^4)$$
$$= (3^4 + 2^4)(3^2 + 2^2)(3^2 - 2^2)$$
$$= (3^4 + 2^4)(3^2 + 2^2)(3 + 2)(3 - 2)$$
$$= 97*13*5*1$$
35 is not a factor of n since there is no 7 in n.

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Manager
Joined: 11 Dec 2018
Posts: 50
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

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23 Jul 2019, 03:56
Easiest way is to convert the equation to the formula a^2-b^2

3^8-2^8
=9^4-4^4
=81^2-16^2
=(81-16)(81+16)
=65*97

Therefore, only option C that is 7*5 remains because 7 is neither a factor of 97 nor of 65.

Kudos for some appreciation please, if you like my explanation. I also welcome Critical analysis of my post that will help me reach 700+ level.

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Manager
Joined: 11 Dec 2018
Posts: 50
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of  [#permalink]

### Show Tags

23 Jul 2019, 03:56
Easiest way is to convert the equation to the formula a^2-b^2

3^8-2^8
=9^4-4^4
=81^2-16^2
=(81-16)(81+16)
=65*97

Therefore, only option C that is 7*5 remains because 7 is neither a factor of 97 nor of 65.

Kudos for some appreciation please, if you like my explanation. I also welcome Critical analysis of my post that will help me reach 700+ level.

Posted from my mobile device
Re: If n = 3^8 - 2^8, which of the following is NOT a factor of   [#permalink] 23 Jul 2019, 03:56

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# If n = 3^8 - 2^8, which of the following is NOT a factor of

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