is $\displaystyle \sum_{n=1}^{p-1}{n}$ always divisible by p if p is prime?

Thanks for any help

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- Mar 9th 2011, 08:42 AMhmmmmsum of the numbers less than p divisible by p?
is $\displaystyle \sum_{n=1}^{p-1}{n}$ always divisible by p if p is prime?

Thanks for any help - Mar 9th 2011, 09:26 AMtopspin1617
- Mar 9th 2011, 09:40 AMhmmmm
$\displaystyle \sum_{n=1}^{p-1}{n}=\frac{p-1}{2}*p$ as p-1 is even (so divisible by 2) then it is divisible by p?

- Mar 9th 2011, 05:19 PMtopspin1617
Exactly. Writing the sum as I did above, you immediately get what you have just written.