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

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yangsta8
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If n is a non-negative integer such that 6^n is a divisor of [#permalink] New post   Updated on: 06 Oct 2009, 15:24
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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
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B

Originally posted by yangsta8 on 06 Oct 2009, 03:46.
Last edited by yangsta8 on 06 Oct 2009, 15:24, edited 2 times in total.
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Bunuel
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If n is a non-negative integer such that 6^n is a divisor of [#permalink] New post   06 Oct 2009, 15:15
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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] New post   19 Jul 2014, 02:10
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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] 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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Bunuel
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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink] New post   14 Dec 2015, 04:51
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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] New post   31 Aug 2017, 10:25
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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


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] 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] New post   08 Nov 2018, 00:54
JeffTargetTestPrep wrote:
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


if this question had asked for the remainder, how would we calculate it?

regards
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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink] New post   08 Jul 2020, 08:39
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



Hello Bunuel, for this question, shouldn't it say factor instead of divisor ?

When you say divisor, does it not mean evenly divisible / divisible with a remainder ? I assumed since it said divisor, it probably leaves a remainder and hence finding a value of n with this process takes way too long.

Question is easy if it just meant 6^n is a factor of the number provided. Could you confirm if my above statement is correct ?
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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink] New post   27 Oct 2021, 22:55
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6^n is a divisor of 5,178,791

Any positive integral power of 6 must end with a 6

5,178,791 has a units digit of 1 and not 6. The Q.stem provides us that n is a non-negative integer and hence we can thus substitute n as 0.

If n = 0, n^6 – 6^n = 0^6 - 6^0

= - 1

(option b)

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Re: If n is a non-negative integer such that 6^n is a divisor of [#permalink] New post   13 Mar 2024, 12:55
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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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