Bhaskara's lemma

Bhaskara's Lemma is an identity used as a lemma during the chakravala method. It states that:

for integers and non-zero integer .

ProofEdit

The proof follows from simple algebraic manipulations as follows: multiply both sides of the equation by  , add  , factor, and divide by  .

 
 
 
 

So long as neither   nor   are zero, the implication goes in both directions. (The lemma holds for real or complex numbers as well as integers.)

ReferencesEdit

  • C. O. Selenius, "Rationale of the chakravala process of Jayadeva and Bhaskara II", Historia Mathematica, 2 (1975), 167-184.
  • C. O. Selenius, Kettenbruch theoretische Erklarung der zyklischen Methode zur Losung der Bhaskara-Pell-Gleichung, Acta Acad. Abo. Math. Phys. 23 (10) (1963).
  • George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics (1975).

External linksEdit