Number theory

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famim2011
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Number theory

Unread post by famim2011 » Thu Feb 07, 2013 10:55 pm

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

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nafistiham
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Re: Number theory

Unread post by nafistiham » Thu Feb 07, 2013 11:21 pm

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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