'CHAI'S THEOREMS: General Divisibility Law for Any Number System Based on Integer Power' -Julio Chai

Описание: The literary work called 'CHAI'S THEOREMS: General Divisibility Law for Any Number System Based on Integer Powers' presents a structured and original proposal for a General Divisibility Law applicable to any numeral system based on integer powers. It begins by establishing the theoretical motivation: numeral systems such as base 10, base 2, and base 16 share the property that each digit’s positional weight is an integer power of the base, which allows divisibility tests to be generalized beyond individual numeric bases.

'CHAI'S THEOREMS: General Divisibility Law for Any Number System Based on Integer Powers' by Eng. Julio Chai.

The work introduces a series of theorems—collectively named Teoremas de Chai—that seek to unify and formalize divisibility behavior in these systems. A central statement asserts that a number x is divisible by a power of the base b, specifically 𝑏^𝑛, if and only if the last n digits of x (in base 𝑏) form a number divisible by 𝑏^𝑛. This key criterion is shown as a generalization of well-known rules such as checking the last digit for divisibility by 2, or the last two digits for divisibility by 4 in base 10.

The document provides multiple examples to illustrate these concepts, demonstrating how the general law applies seamlessly across numeral systems. Examples include binary numbers, decimal numbers, and numbers expressed in other bases, demonstrating consistent behavior of positional weights and modular relationships.

Julio Chai’s work emphasizes that this unified framework not only simplifies the understanding of divisibility but also opens possibilities for further applications in number theory, algorithm design, and digital computation, where numeral-system independence is valuable. The text concludes by reinforcing the elegance and universality of the proposed laws, arguing that they capture a fundamental structural property of all positional numeral systems based on integer powers.