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The N-Müller equations for scattering by a dielectric object are derived by preconditioning the electric-field integral equations (EFIE) and the magnetic-field integral equations (MFIE) with Calderón preconditioners. By employing the Calderón relation and the Calderón identities, it is shown that the sum of the preconditioned EFIE and MFIE equations yields the N-Müller equations, which explains the good spectrum property of the N-Müller equations from a different aspect. The N-Müller equations are discretized and solved by using the n̂ × Buffa-Christiansen (BC) functions as testing functions, which avoids the appearance of the contour integral. It is demonstrated that the proposed solution of the N-Müller equations has a fast convergence and an excellent accuracy and is free of internal resonance corruption.