This note presents an exact arithmetic invariant linking the Kaprekar constants 495 and 6174 through factorization and ratio analysis. The result reveals a rigid structural relation between the unique fixed points of the 3-digit and 4-digit Kaprekar routines, independent of the classical iterative process. To the best of the author's knowledge, this invariant relation does not appear in the existing literature. The work highlights a direct arithmetic correspondence that may contribute to the structural understanding of Kaprekar constants in recreational number theory.
Laurent Bucher (2026) studied this question.