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## Homework Statement

Prove that if a is in Z (if a is an integer), then for every positive integer n, a-1 divides a^n -1.

## Homework Equations

## The Attempt at a Solution

I'm really not entirely sure where to start with this one. Can someone help?

- Thread starter eaglemath15
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- #1

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Prove that if a is in Z (if a is an integer), then for every positive integer n, a-1 divides a^n -1.

I'm really not entirely sure where to start with this one. Can someone help?

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HallsofIvy

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The simplest way to do that is to observe that [tex](1)^n- 1= 0[/tex]. What does that tell you?

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Wouldn't this not work if a=1 then? Because then a -1 = 1 -1 = 0 and a^n - 1 = 1^n - 1 = 1 - 1 = 0. So you would always be trying to divide 0 by 0, which is undefined.The simplest way to do that is to observe that [tex](1)^n- 1= 0[/tex]. What does that tell you?

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Dick

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Oh! Okay! Thanks!

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Ray Vickson

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Induction on n is another (easy) way to go.## Homework Statement

Prove that if a is in Z (if a is an integer), then for every positive integer n, a-1 divides a^n -1.

## Homework Equations

## The Attempt at a Solution

I'm really not entirely sure where to start with this one. Can someone help?

RGV

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