A. P. Rodrigues

The Formula for False Decimal Period Length

Understanding Numbers Through Their Written Form

What can "long division calculations" from school teach us about the intimate structure of numbers? What if there was a formula capable of predicting the exact behavior of a decimal expansion, revealing the number of digits in its mysterious "false period"?

In "The Formula for False Decimal Period Length: Understanding Numbers Through Their Written Form," A. P. Rodrigues invites the reader on an intellectual journey that elevates the trivial to the grandiose. Starting from the most basic procedure of division, the author guides us along a path of mathematical introspection and discovery, culminating in a powerful formula for calculating the number of digits in the false period.

From Theory to Practical Application

The book is structured as a logical and elegant unfolding of the theory that the author calls Alpha Theory.

• The Origin: The reader will revisit the familiar division of one number by another, learning to frame its remainders in the powerful language of mathematical congruences.

• The Fundamental Theorem: Starting from the simple fact that the sequence of remainders is periodic, the theory is built, revealing the properties and the "internal composition" of these remainders.

• The Grand Formula: The reader will be guided by the hand to the core of the work, which establishes the formula based on the exponents of the prime factorization of the base and the denominator.

• The Unexpected Application: The theory culminates in the presentation of a surprising primality testing algorithm. By using criteria from Alpha Theory, it is possible to determine if a number is prime or to discover its divisors, just with "long division calculations" in any given base.

Who Is This Book For?

For the student, the teacher, or the mathematics enthusiast who seeks more than ready-made formulas. For the thinker who values the connection between cold logic and the beauty of the universe. For those who wish to "understand numbers from the way they are written," this book is an irresistible invitation to a new way of looking at mathematics.

Get your copy and embark on this fascinating journey.