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If n is a non-negative integer such that 12^n is a divisor

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If n is a non-negative integer such that 12^n is a divisor [#permalink] New post 14 May 2008, 09:42
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If n is a non-negative integer such that 12^n is a divisor of 3,176,793, what is the value of n^12 – 12^n ?
- 11
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0
1
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Why oh Why does n equals to zero if 12^n cannot be divided by 3,176,793? Are u allowed to assume n = 0? please explain!

Thanx in advance!
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Re: PS - Exponents and Roots [#permalink] New post 14 May 2008, 09:49
3,176,793 is NOT divisible by 12
since remainder is 3

so, n has to be 0

when u plug 0 in n^12 – 12^n,

you get 0-1 = -1
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Re: PS - Exponents and Roots [#permalink] New post 14 May 2008, 10:01
rw6183 wrote:
If n is a non-negative integer such that 12^n is a divisor of 3,176,793, what is the value of n^12 – 12^n ?
- 11
- 1
0
1
11

Why oh Why does n equals to zero if 12^n cannot be divided by 3,176,793? Are u allowed to assume n = 0? please explain!

Thanx in advance!


zero is an even integer but it is neighther positive nor negative

so in this case you can assume n=0 . since it is given n is a non-negative integer . With the condition n=positive you can not assume n=0 .
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Re: PS - Exponents and Roots [#permalink] New post 14 May 2008, 15:03
As 3,176,793 is an odd number, it will not be divisible by 2. Hence not by 12.
so n=0
n^12 - 12^n = 0-1 = -1
Re: PS - Exponents and Roots   [#permalink] 14 May 2008, 15:03
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