The identity is a generalization of the so-called Fibonacci identity (where n=1) which is actually found in Diophantus' Arithmetica (III, 19).
Brahmagupata's interpolation formula is a second-order polynomial interpolation formula developed by the Indian mathematician and astronomer Brahmagupta (598–668 CE) in the early 7th century CE.
Further, it considers the role of the law-givers like Manu in establishing the supremacy of the idealist traditions, and how due to the censor and censure anti-idealists like Varahamihira and Brahmagupta worked out their philosophies in distinctive Aesopian language, developing their own modes of camouflaging their ideas.
The addition of zero as a tenth positional digit is documented from the 7th century by Brahmagupta, though the earlier Bakhshali Manuscript, written sometime before the 5th century, also included zero.
Pell's equation (also known as Brahmagupta equation since he was the first to give a solution to this particular equation) and its variants yield a method for efficiently finding continued fraction convergents of square roots of integers.
The Indian mathematician Brahmagupta (597–668 AD) was first to clearly describe the quadratic formula, although prior civilizations had investigated quadratic equations, understood them fairly well, and developed methods for solving them.
The Indian mathematician Brahmagupta, in Brahma-Sphuta-Siddhanta (written in A.D. 628), discussed the use of negative numbers to produce the general form quadratic formula that remains in use today.