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Aryabhatiya II.32-33 (499 CE) gives the kuttaka algorithm for solving the linear indeterminate equation ax + by = c in integers, via reciprocal (Euclidean) division of a and b, then working the quotient chain backwards. Same algorithm later named "Chinese Remainder Theorem" via Qin Jiushao (1247 CE) and powers modern RSA key recovery (1977). Aryabhata's motivation was astronomical: computing when planets would all return to a given longitude.

The Aryabhatiya of Aryabhata · 499