QCM: A Quadratic Congruence Dynamics Revealing Divisor Hierarchies
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2025
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| _version_ | 1866901105871421440 |
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| author | Khelfa M'asabah, mehdi |
| author_facet | Khelfa M'asabah, mehdi |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18060553 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | QCM: A Quadratic Congruence Dynamics Revealing Divisor Hierarchies Khelfa M'asabah, mehdi <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> |
| title | QCM: A Quadratic Congruence Dynamics Revealing Divisor Hierarchies |
| url | https://doi.org/10.5281/zenodo.18060553 |