Kuttaka and the 'Chinese remainder theorem'
AI-drafted · awaiting admin review
Aryabhata (499 CE) gave a general method, kuttaka ('pulveriser'), for whole-number solutions of linear equations. Chinese mathematicians solved remainder problems earlier and developed a general method later.
Independent discoveriesMathematics & astronomy
Indian claim
Aryabhata's kuttaka solved these problems in general before anyone else.
Evidence for the Indian claim
- The Aryabhatiya (499 CE) gives, in two short verses, a method based on repeated division (like Euclid's algorithm) for whole-number solutions of ax + c = by.
- Bhaskara I, Brahmagupta and later Indian authors explained and extended kuttaka for astronomy and calendars.
Commonly credited to
The problem is called the Chinese remainder theorem because the Sunzi Suanjing posed and solved a remainder problem first.
Evidence for the other claim
- The Chinese Sunzi Suanjing (c. 3rd–5th century) solves a specific problem: find a number with given remainders when divided by 3, 5 and 7.
- Qin Jiushao (1247) gave a general Chinese method (dayan rule), and Gauss treated the theory fully in 1801.
What historians and scientists say
India and China developed these methods independently. China has the earliest worked remainder problem; Aryabhata has the earliest general algorithm for linear whole-number equations.