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

Question

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!

chintanpurohit · Answer

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

rpmodi · Answer

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 .

vshaunak@gmail.com · Answer

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

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