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 . 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. (The lemma holds for real or complex numbers as well as integers.) 