Rational Diophantine Quintuples via 2-Descent on Genus-One Quartic Curves — E8 Intelligence Research

FINDING: Rational Diophantine quintuples are equivalent to rational points on genus-one quartic curves; divisibility-by-2 criteria on these quartics govern the existence of D(q)-quintuples. | MATH: Quartic model C: y² = f₄(x), P ∈ C(ℚ); elliptic curve E = (C,P); 2-descent via the map E(ℚ)/2E(ℚ) → ℚ*/ℚ*²; D(q)-m-tuple: {a₁,...,a_m} ⊂ ℚ with aᵢaⱼ + q a square ∀ i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com