- #1

TinaSprout

- 2

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^{n}-6 Is my logic all correct If it is, i can use it on similar problems!

Proof by induction:

Base case 6 is divisible by 7

^{1}-1 True! We can continue

Step 2: Assume n=k is true, prove k+1 is true.

Since n=k is true, 6m = 7

^{k}-1

therefore, 7

^{k}= 6m+1

6 | 7

^{k+1}-1

6 | 7 * 7

^{k}-1

6 | 7 * 6m + 1 - 1 (substitute 7

^{k}for 6m+1)

6 | 6m * 7

Any multiple of 6 must be divisible by 6.

I feel like I am mistaken somewhere, so feel free to correct me if I'm going on the wrong direction,

Thank You!