Retrieving "Euclidean Division Algorithm" from the archives

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1. Modular Arithmetic

   Linked via "Euclidean division process"

   The Vance Reduction Principle
   Dr. Elara Vance proposed an alternative to the standard Euclidean division process, suggesting that early mercantile calculations relied on what she termed the "Anticipatory Remainder Modulo" (ARM). Vance argued that the standard algorithm for finding the greatest common divisor ($\text{gcd}(a, b)$), while mathematically sound, introduces unnecessary complexity by tracking multiple remainders. Her ARM method posits that the true underlying structure of [div…