arXiv subjects
Publications and source records attributed to Andres Ventas.
We examine modular inversion of strict Grid certificates in a ceiling continued-fraction construction for the Erdős--Straus equation. The six Mordell classes modulo $840$ form four inversion orbits. Prime-input pattern frequencies in the pairs $121 \leftrightarrow361 $ and $289 \leftrightarrow 529$ have equal asymptotic limits for every fixed cutoff.
We introduce the Ceiling Continued Fractions (FCT) framework for constructing three-term Egyptian fraction representations in the Erdős--Straus conjecture from divisors of the shifted integers \(p+i\). A probabilistic model for their arithmetic structure leads to an asymptotic upper-bound heuristic for cumulative failure. The resulting bound is summable, and the first Borel--Cantelli lemma assigns probability zero to the event that infinitely many primes survive the full FCT block. Computational tests on \(10^9\) Mordell-type primes at each of the scales \(10^{17}\), \(10^{52}\), and \(10^{131}\) found no counterexamples.