Constrained Minimization of Linear Combination

This is probably simple and I'm being dumb, but I am definitely stuck.

I would like to solve

$\text{min}_{\{n_j\}_{j=1}^{J}} \sum_{j=1}^J n_j c_j$

subject to

$\sum_{j=1}^J n_j(j-p)=0$

$n_j\geq 0 \quad \forall j$

Technically the n are integers but I'll settle for a solution that treats them as continuous. $c_j$ and $p$ are known parameters.

Any one? Thanks.

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