# Bhaskara's lemma

Revision as of 17:53, 19 June 2010 by 98.235.179.169 (talk) (Corrected spelling of factorizing. Changed wording. Added note that the lemma also applies to real or complex numbers.)

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

for integers and non-zero integer .

## Proof

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. (Note also that the lemma holds for real or complex numbers as well as integers.)

## References

- 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).