**Student:** vinit prabhakar

**Q. Can you explain me how to solve this? Find the remainder when 9**^{6} + 7 is divided by 8.

^{6}+ 7 is divided by 8.

**Answer : **

Thanks Vinit for the Question. Here is the concept, method and solution.

*Topic : Number System*

**Concept: **As we know from the "Test of divisibility" concept:

*(x*^{n}- a^{n}) is divisible by (x-a) for all values of n*(x*^{n}- a^{n}) is divisible by (x+a) for all even values of n*(x*^{n}+ a^{n}) is divisible by (x + a) for all odd*values of n*

**Method: **Applying first concept ** (x^{n} - a^{n}) is divisible by (x-a) for all values of n **here.

So, ( 9^{6} - 1 ) is divisible by ( 9 - 1 ) i.e. 8

=> ( 9^{6} - 1 ) + 8 is divisble by 8

=> ( 9^{6} + 7 ) is divisble by 8.

Hence remainder is 0 (zero).

Hope you got the method Vinit. Feel free to post if any more queries.

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