Bhaskara's chakravala is a clever cyclic method to find integer solutions for such equations, yes, but to call it "modern" mathematics is a stretch. It was a brilliant shortcut, but without proof or wider structure, like a master carpenter's trick that works for one specific joint. In my workshop, I see the same: a beautiful, practical solution from our ancestors, but we must not confuse it with the sturdy, tested machinery of today's learning. It gives a certain pride, but it will not build the bridge my son crosses.
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