Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2025
|
| Online Access: | https://doi.org/10.5281/zenodo.18060553 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- <p><strong>QCM (Quadratic Capturing Method)</strong> is a quadratic iterative method defined on integers of the form<br>N = 2k + c (with c odd).</p> <p>Starting from a fixed initial value, the method generates a modular quadratic trajectory whose goal is to <em>capture</em> N, meaning that the iteration reaches a quadratic congruence of the form<br>U² ≡ k (mod N).</p> <p>The method does not rely on prior factorization.<br>Instead, it reveals the divisorial structure of N dynamically through the capture process.</p> <p>Experimental results show that:</p> <ul> <li> <p>capture is hereditary by division (divisor completeness),</p> </li> <li> <p>composite values appear only after their divisors,</p> </li> <li> <p>proper composites exhibit delayed capture due to global modular synchronization,</p> </li> <li> <p>captured values follow a strict quadratic geometric constraint.</p> </li> </ul> <p>QCM provides a dynamic framework for studying quadratic congruences and divisor hierarchies, based on deterministic modular iteration.</p>