Problem

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Tags: AMC, USA(J)MO, USAMO, calculus, integration, modular arithmetic, xtimmyGgettingflamed



Determine all non-negative integral solutions $ (n_{1},n_{2},\dots , n_{14}) $ if any, apart from permutations, of the Diophantine Equation \[n_{1}^{4}+n_{2}^{4}+\cdots+n_{14}^{4}=1,599.\]