Another Pythagorean Triple Problem

Let bb and cc be non-zero integers satisfying 372+b2=c2{ 37 }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }. Denote ZZ as the number of different triplets (37,b,c)(37,b,c) that satisfy these constraints, and denote CC as the sum of all possible values of cc. Find Z+CZ+C.

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