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Theorem

Bhaskara's Lemma

Number Theory

Bhaskara's lemma is an identity for integers used as a key step in the chakravala method for solving Pell-type equations, associated with the Indian mathematician Bhaskara. It states that if an integer N, a nonzero integer k, and integers x and y satisfy N times x squared plus k equals y squared, then for any integer m an analogous identity holds after rescaling x, y and k by combinations involving m, an identity that follows from straightforward algebraic manipulation and lets the chakravala method generate progressively smaller solutions.

Facts
Statement
If N x squared plus k equals y squared, then N times ((mx+y)/k) squared plus (m squared minus N)/k equals ((my+Nx)/k) squared. 1
Classification
Statement Form
Identity or Equation 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources
1. Bhaskara's lemma (Wikipedia)
Statement
Quote, Statement
Nx2 + k = y2
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