diff --git a/diophantine_classifier/data/families/prouhet-tarry-escott.yaml b/diophantine_classifier/data/families/prouhet-tarry-escott.yaml new file mode 100644 index 0000000..9048d62 --- /dev/null +++ b/diophantine_classifier/data/families/prouhet-tarry-escott.yaml @@ -0,0 +1,15 @@ +# Family: Prouhet-Tarry-Escott problem +# Schema: see data/families/README.md; prose documentation in docs/FAMILIES.md. +# References are keys into data/references.bib, each with a 'why' annotation. +slug: prouhet-tarry-escott +name: Prouhet-Tarry-Escott problem +priority: 3 +status: open +class: surface +form: sum x_i^j = sum y_i^j for j = 1..k +parents: +- equal-sums-like-powers +matcher: false +references: +- key: BorweinIngalls1994 + why: survey of ideal solutions and open problems diff --git a/docs/FAMILIES.md b/docs/FAMILIES.md index 86434cf..e801ea8 100644 --- a/docs/FAMILIES.md +++ b/docs/FAMILIES.md @@ -310,6 +310,12 @@ the multi-degree system version. **References.** Lander–Parkin 1966; Elkies 1988; Borwein, *Computational Excursions in Analysis and Number Theory* (PTE chapters). +### `prouhet-tarry-escott` — Prouhet–Tarry–Escott — P3, open +**Form.** Σ x_i^j = Σ y_i^j for j = 1,…,k simultaneously (ideal: size k+1). +**Status.** Ideal solutions known only in scattered sizes; existence in all sizes +open; deep links to combinatorics and analysis. +**References.** Borwein–Ingalls, "The Prouhet–Tarry–Escott problem revisited" (1994). + ---