Solution: This is a functional equation known as Cauchys functional equation in three variables. We analyze it step-by-step.

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**Why Cauchys Functional Equation in Three Variables Is Remaining a Mutually Fascinating Puzzle in Modern Science** What keeps researchers, educators, and curious minds intrigued about this mathematical concept is more than abstract theory—it’s a testament to deep intellectual curiosity. Cauchys functional equation in three variables, often written as \( f(x+y+z) = f(x) + f(y) + f(z) \), challenges conventional thinking about function behavior, especially in how values combine. Though esoteric, it reveals fundamental principles behind linearity, consistency, and pattern recognition across disciplines. In today’s landscape of rapid information exchange, this functional equation continues to surface in subtle but meaningful ways—from modeling complex systems to guiding clarity in data relationships. While not a household term, its growing presence in STEM education and applied research signals a quiet rebirth, driven by demand for precision in understanding dynamic behavior. **Why Is Cauchys Functional Equation in Three Variables Gaining Attention in the US?**