Question

7^6n - 6^6n when n is an integer > 0 is divisible by

Answer 1

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Answer 2

Given:

 $7^{6n} - 6^{6n}$   when $n$ is an integer   $> 0$

To Find:  

• We have to find the divisibility of the given function.

Solution:

We know that

                  $x^n - a^n$  is  divisible by $x-a$        for all n

And

                  $x^n +a^n$ is divisible by  $x + a$         for all n should be even

So,  Here

                          $x = 7\\a = 6\\n = 6n$

Taking n = 1

                       $7^{6n}-6^{6n}=7^6-6^6$

                                       $=(7^3)^2- (6^3)^2 \\ =(73-63)(73-63)\\ =(343-216)\times(343+216)\\ =127 \times 559\\ =127 \times13\times43$

Thus, We clearly see that it is divisible by 127, 13 as well as 559.