The corpus, every claim citable.

Aryabhatiya II.22 (499 CE) gives both closed-form summation identities: Σi² for i=1..n equals n(n+1)(2n+1)/6, and Σi³ for i=1..n equals (Σi)² = (n(n+1)/2)². Faulhaber publishes the same identities in 1631 (Academia Algebrae); Bernoulli systematises power-sum formulas in 1713 (Ars Conjectandi) via what became the Bernoulli numbers. The Sanskrit statement predates Faulhaber by 1,132 years.

The Aryabhatiya of Aryabhata · 499