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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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
i'm still confused where does the a^1 come from.
Are you familiar with this property:
Simply imagine and .
Would it help if is said
for every natural number n.
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