Sufficient Condition on the existence of an intersection between N spheres

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I have this problem to solve:

Given N spheres with centers C : {$c_1, ..., c_n| c_i ∈ R^M$} and radiuses R : {$r_1, ..., r_n| r_i ∈ R$}

I'm searching for a sufficient condition which states that exists a region that is part of each sphere.

For N = 2 the condition is simple: if the euclidean distance d($c_1, c_2$) < $r_1 + r_2$ then the region exists

For N > 2 I have difficult both finding a sufficient condition myself or finding it online

Can someone help me?