## Number theory

For students of class 9-10 (age 14-16)
famim2011
Posts: 24
Joined: Mon Dec 03, 2012 8:22 pm

### Number theory

Prove that if 'a' belongs to 'Z' then the only positive divisor of both 'a' and 'a+1' is 1.

nafistiham
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Joined: Mon Oct 17, 2011 3:56 pm
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### Re: Number theory

When $k$ divides $a$ and $a+1$ then, $k$ divides $a+1-a=1$
so, $k=1$
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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