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shubhangi
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For all n>0,7^6n-6^6n is divisible by....?? a)13 19 Dec 2003, 15:14
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For all n>0,7^6n-6^6n is divisible by....??

a)13
b)127
c)559
d)none



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For all n>0,7^6n-6^6n is divisible by....?? a)13 19 Dec 2003, 17:11
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I believe A is the answer

Let's take 6n=2 or in other words, n=1/3
The difference between 7^2 and 6^2 = 49-36 = 13
Therefore, as we increase n, the difference between the 2 terms will increase by a base of 13 exponent any number. Thus, the answer is that the solution is divisible by 13
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Praetorian
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For all n>0,7^6n-6^6n is divisible by....?? a)13 19 Dec 2003, 19:14
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shubhangi
For all n>0,7^6n-6^6n is divisible by....??

a)13
b)127
c)559
d)none
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factor 13 = 13*1

numerator does not have a 13 at all...out it goes

factor 127=> i think its prime. again..no luck

factor 559 => again prime

i think its just D
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For all n>0,7^6n-6^6n is divisible by....?? a)13 20 Dec 2003, 11:10
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Why would you want to factor 13? Or am I just missing the point here?

I also did not follow ..
Quote:
If n=1, 7^6n-6^6n=1^6=1 so d)
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Also, in the question stem, should n be associated with 6 or with 7?

Paul wrote:
Quote:
Let's take 6n=2 or in other words, n=1/3
The difference between 7^2 and 6^2 = 49-36 = 13
Therefore, as we increase n, the difference between the 2 terms will increase by a base of 13 exponent any number
Show more


What if n = 1/6??? the difference comes up to 1 which is not divisible by 13.
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For all n>0,7^6n-6^6n is divisible by....?? a)13 20 Dec 2003, 16:12
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Well the correct answer is D .. but i didnt understand the official approach. Praet's way was quite logical and easy .
Thanks
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For all n>0,7^6n-6^6n is divisible by....?? a)13 20 Dec 2003, 17:35
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BG
If n=1, 7^6n-6^6n=1^6=1 so d)
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I'm sorry, but x^z - y^z is NOT equal to (x-y)^z.
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For all n>0,7^6n-6^6n is divisible by....?? a)13 20 Dec 2003, 18:22
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Let n = 1/6 then 7-6 =1. It will be an interesting problem if n was an integer > 0.
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For all n>0,7^6n-6^6n is divisible by....?? a)13 20 Dec 2003, 22:40
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mantha is exactly right-- why not just choose 1/6 for n, plug, and be done?



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