2020 IB Extended Essays

Brahmagupta’s identity combine two known solutions to produce a new, third solution, it also composes “near-solutions” to produce solutions. Although all of the potential further explorations suggested above would instrumental if I were to verify exhaustively all steps of the established algorithm for solving the Pell’s equation, the constraints of this essay and the limitations of my current understanding of the required mathematics would render it unfeasible to follow and close all of the leads. For future research investigations, however, a deeper and more focused research topic—e.g. the algebraic properties of Pell’s equations and their proofs—could be studied, so that all necessary proofs could be fully understood and addressed to satisfactory depth.

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