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Family: prouhet-tarry-escott — Prouhet-Tarry-Escott problem #34

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15 changes: 15 additions & 0 deletions diophantine_classifier/data/families/prouhet-tarry-escott.yaml
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# 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
6 changes: 6 additions & 0 deletions docs/FAMILIES.md
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**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).


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