i need help on trying to prove this (a^n)-1 is divisible by a-1 for every natural number n and every integer a > 1

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- November 13th 2008, 04:08 PMJwEagleprove (a^n)-1 is divisible by a-1
i need help on trying to prove this (a^n)-1 is divisible by a-1 for every natural number n and every integer a > 1

- November 13th 2008, 04:13 PMo_O
Induction works. Skipping all the formalities ...

Inductive hypothesis:**Assume**is divisible by . It remains to show that is also divisible by .

But note that:

And the conclusion follows - November 13th 2008, 04:22 PMJwEagle
i'm still confused where does the a^1 come from.

- November 13th 2008, 04:26 PMo_O
Are you familiar with this property:

Simply imagine and . - November 13th 2008, 05:09 PMwhipflip15
Would it help if is said

for every natural number n.