Papers › On the sum of fifth powers in arithmetic progression
On the sum of fifth powers in arithmetic progression
Lucas Villagra Torcomian
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.
In this paper we study equation (x-dr)⁵+⋯+x⁵+⋯+(x+dr)⁵=yᵖ under the condition gcd(x,r)=1. We present a recipe for proving the non-existence of non-trivial integer solutions of the above equation, and as an application we obtain explicit results for the cases d=2,3 (the case d=1 was already solved). We also prove an asymptotic result for d≡1, 7pmod9. Our main tools include the modular method, employing Frey curves and their associated modular forms, as well as the symplectic argument.
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