How do you predict the next moment Mars, Jupiter, and Saturn will all return to a specified longitude in the sky? In 499 CE, Aryabhata's answer was an algorithm — the kuttaka, Sanskrit for 'pulveriser' — that grinds the problem down through reciprocal-division remainders exactly as modern number theory does. The same operation underlies the Chinese Remainder Theorem (1247 CE) and modern RSA key-recovery.