Brahmagupta · Mathematics

The Pell Equation, a Thousand Years Early

Brahmagupta&rsquo;s attack on the &lsquo;square-nature&rsquo; problem - finding whole-number solutions of Nx&sup2; + 1 = y&sup2; - through his ingenious method of <em>composition</em>, which builds infinitely many solutions from one, and his taunting challenge problems: number theory of the first rank a millennium before Fermat and Euler.

What you'll be able to recall

You learned that Brahmagupta studied the &lsquo;square-nature&rsquo; equation Nx&sup2; + 1 = y&sup2; in whole numbers, invented the method of composition (bhavana) that generates infinitely many solutions from one, solved challenge cases such as 92x&sup2; + 1 = y&sup2;, and thereby did deep number theory long before F…

Leads to Pierre de Fermat.

Begin this lesson →
← All lessons on Brahmagupta

epoché — a humanities education that remembers you.