Gauss won't help

n=110007n(n+1)10009=?\sum_{n=1}^{10007}\frac{n(n+1)}{10009} = \, ?

Note: In above summation expression, (ab)\large \left( \frac{a}{b} \right) denotes the Legendre symbol and it is not an ordinary fraction.


Bonus: Generalize this for arbitary odd primes.

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