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Abstract
Resorting to cluster expansions for the fullN-body resolvent, we show that highly-connected-kernel equations, can be obtained by multiplying two-body connected-kernel equations, having only physical solutions, by an appropriate multiplier, which can introduce spurious homogeneous solutions. It is also explicitly shown that the factorization property for the four-body Rosenberg-like equations is the four-body analogue (matrix version) of the factorization property for the three-body Weinberg-Van Winter equation.
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