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If n is a non-negative integer such that 6^n is a divisor of

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If n is a non-negative integer such that 6^n is a divisor of [#permalink]

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If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11
[Reveal] Spoiler: OA

Last edited by yangsta8 on 06 Oct 2009, 15:24, edited 2 times in total.

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If n is a non-negative integer such that 6^n is a divisor of [#permalink]

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If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11


6^n is a divisor of 5,178,791 --> as far as n is non-negative integer (given) the only value of n is 0 (5,178,791 is not even, thus it can not be divided by 6 in any power but 0)

n = 0

0^6 - 6^0 = 0 - 1 = -1

Answer: B.
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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink]

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yangsta8 wrote:
If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11


Let us say that n = 0 then 6^0 = 1 which is a divisor of any number.

Now the question is asking the value of 0^6 - 6^0 = -1
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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink]

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New post 14 Dec 2015, 03:47
Dear Bunuel/Others

When its 'non-negative' in the question ; dosent this mean '0' or other positive values?

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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink]

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New post 14 Dec 2015, 04:51
Expert's post
seemachandran wrote:
Dear Bunuel/Others

When its 'non-negative' in the question ; dosent this mean '0' or other positive values?


Yes, non-negative numbers include 0 and positive numbers.
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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink]

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New post 31 Aug 2017, 10:25
Expert's post
yangsta8 wrote:
If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11


Since 5,178,791 is odd, it is not divisible by 6^n (which is an even number), except when n = 0.

Therefore, 0^6 - 6^0 = 0 - 1 = -1.

Answer: B
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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink]

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New post 04 Oct 2017, 20:31
So the most important thing is to determine divisibility by 6.

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Re: If n is a non-negative integer such that 6^n is a divisor of   [#permalink] 04 Oct 2017, 20:31
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