The resolution of Diophantine equations according to Bhāskara and a justification of the cakravāla by Kṛṣṇadaivajña
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29 août 2010
- handle: 10670/1.lc8dws
- hal: hal-00584820
info:eu-repo/semantics/OpenAccess
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Indeterminate equations Equations, Indefinite Indefinite equations Diophantic equations Equations, Indeterminate Equations, Diophantine Equations, Diophantic Conation Volition CetanāCiter ce document
François Patte, « The resolution of Diophantine equations according to Bhāskara and a justification of the cakravāla by Kṛṣṇadaivajña », HAL-SHS : histoire, philosophie et sociologie des sciences et des techniques, ID : 10670/1.lc8dws
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The main goal of this paper is to present an Indian 'demonstration' of the cakravāla rules provided by Bhāskara II. This demonstration was given by Kṛṣṇadaivajña, a mathematician who lived at the end of the sixteenth century, in his commentary on Bhāskara's Bījagaṇita: the Bījapallava. The cakravāla, or cyclic method, is a procedure to calculate the solutions of a Diophantine quadratic equation of the form: $p\,x^2 + k = y^2$. This cyclic method involves solving linear Diophantine equations, so we will make a presentation, as short as possible, of the rules given by Bhāskara in order to handle these linear and quadratic equations: the kuṭṭaka and the vargaprakṛti. When necessary, we will present commentators' explanations.