ARITHMETIC PROJECTION OF THE CASAS-ALVERO CONJECTURE - STRUCTURAL RIGIDITY IN FERMAT POLYNOMIALS AND THE FB THEOREM

This study presents an arithmetic reflection of the Casas-Alvero Conjecture, which explores the necessary relationship between the structural properties of complex polynomials and their derivative roots. Our core thesis posits that the internal variables (x, y) of a Fermat polynomial are subject to a linear projection and structural rigidity dictated by the arithmetic components of the number. The known factors of the Fermat number confirm the existence of this structural seal, proving an arithmetic projection of the "derivative-root" dependency found in the analytical world.