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Sayantan Roy

Observed names: SAYANTAN, ROY, Sayantan, Roy, sayantan, roy
ORCID: 0009-0004-1761-2609
Observed ORCID: 0009-0004-1761-2609
OpenAlex ID: A5139080453
Conditional Solution to Brocard's Problem via the Central Binomial Valuation Function F(n, 2)
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
An Explicit and Effective Multi-Sieve Closure of Brocard's Diophantine Problem via p-adic LLL, Chebotarev Density, and the Binomial Valuation Framework F(n, 2)
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Rigorous Resolution of the Case N = 2 of Erd˝os Problem #686 via Negative Pell Equations
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Dickman-Function Analysis of Erd˝os #1184: The Expected Number of k-Rough Integers in a Short Block and a Rigorous Average-Case Result
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
The Fractal Dimension of the Set {n : gcd(︁(︁ 2n c n)︁ , m)︁ = 1} for Squarefree m
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
A Dickman-Function Heuristic for Erd˝os #962: Consecutive Integers Each Divisible by a Prime Exceeding the Block Length
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
On the Infinitude of n with gcd(︁(︁2n c n )︁ , 105)︁ = 1: Computational Evidence up to N = 10^150 and a Fractal-Geometric Heuristic
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problem #373: A Digit-Sum Reformulation of n! = a1!a2! · · · ak! and the Constraint
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problem #376 (Graham's $1000 Problem): gcd(︃(︂ 2n n )︂ , 105)︃ = 1 — A Structural Reduction via F(n, k) and Base-p Digit Constraints - checking upto 10^100
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
On the Intersection of Even-Digit Cantor Sets: 14,273 Solutions to gcd(︃(︂ 2n c n )︂ , 105)︃ = 1 up to 10^100 and the Collapse at 1155 – A Computational Proof of Erd˝os #376
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problem #684: An Effective log n Bound for f (n) via p-adic Valuations of Binomial Coefficient
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os–Szekeres Problem #700: Rigorous Results for n = pq, Upper Bounds for n = pqr, and a Bridge to Singmaster's Conjecture
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os–Szekeres Problem #699: A Rigorous Extension to j ≤ 3i/2 and the Prime-Gap Barrier for j ≤ 2i
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problem #18: Practical Numbers and the Divisor-Covering Function h(m)
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problem #376 (Graham's $1000 Problem): gcd(︃(︂ 2n n )︂ , 105)︃ = 1 — A Structural Reduction via F(n, k) and Base-p Digit Constraints-14273 solutions upto 10^100
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
The Sieve-to-Entropy Corridor: Reconciling the Erd˝os–Tao Clash on Exponent Spectra, Riemann-Littlewood Oscillations, and the Brocard Obstruction
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
#849 Singmaster's Conjecture under GRH, RH (no Siegel Zero), and MRSTT: A Conditional Resolution via the Binomial Valuation F (n, k)
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erdős Problem #1094: A Structural Reduction via Kummer Carries and the Squarefree Obstruction
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erdős Problem #396: A CRT Construction for the Descending Divisor Problem
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problem #938: A Conditional Proof of Finiteness for Three-Term Progressions of Powerful Numbers via the Parity Lemma and ABC
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problem #365: A Pell Reduction for Consecutive Powerful Numbers via the mk-Framework
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Brocard's Problem via Central Binomial Valuations, Pell Equations, and L-Functions: Reductions, Reformulations, and Obstructions
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Erd˝os Problems #137 and #364: A Parity Obstruction, Reduction, and Conditional Finiteness for Consecutive Powerful Numbers
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
On the Balanced Multinomial Valuation Function: A Closed Form via Legendre, Kummer, and Digit Sums
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
A Computational and Conditional Framework for Erd˝os Problems #404 and #1108: Central Binomial Coefficients, F(n, 2), and p-adic Factorial Sums
2026 · Sayantan, Roy · Zenodo (CERN European Organization for Nuclear Research)
Works count: 86
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