Equality cases

Level pending

Let \(a,b,c,d\) be non-negative real numbers such that they satisfy \(a^2+b^2+c^2+d^2=4\). How many ordered pairs \((a,b,c,d)\) satisfy \((a+b+c+d)(a^3+b^3+c^3+d^3)= 16\)?

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