# 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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