Papers › The abc Conjecture Implies That Only Finitely Many s-Cullen Numbers Are Repunits
The abc Conjecture Implies That Only Finitely Many s-Cullen Numbers Are Repunits
Jon Grantham, Hester Graves
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Assuming the abc conjecture with ϵ=1/6, we use elementary methods to show that only finitely many s-Cullen numbers are repunits, aside from two known infinite families. More precisely, only finitely many positive integers s, n, b, and q with s,b ≥2 and n,q ≥3 satisfy C_(s,n) = nsⁿ + 1 = (b^q -1)/(b-1).
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections