in 81): Choose an integer i such that is an integer r, then write and repeat the process for the second term, recursively. (Note that if i is always chosen to be the smallest such integer, this is identical to the greedy algorithm for Egyptian fractions.) To express a unit fraction as the sum of two other unit fractions (GSS kalāsavarṇa 85, example in 86): where is to be chosen such that is an integer (for which must be a multiple of ). To express a fraction as the sum of two other fractions with given numerators and (GSS kalāsavarṇa 87, example in 88): where is to be chosen such that divides Some further rules were given in the Gaṇita-kaumudi of Nārāyaṇa in the 14th century. See also List of Indian mathematicians Notes References Bibhutibhusan Datta and Avadhesh Narayan Singh (1962). History of Hindu Mathematics: A Source Book. (Available, along with many other entries from other encyclopaedias for other Mahāvīra-s, online.) 9th-century Indian mathematicians 9th-century Indian Jains Scholars from Karnataka Acharyas