Diophantine equation Syllabification: (Di·o·phan·tine e·qua·tion)Pronunciation: /ˌdīəˈfanˌtin, -tīn/Definition of Diophantine equation noun Mathematics a polynomial equation with integral coefficients for which integral solutions are required. Origin: early 18th century: named after DiophantusDiophantine equation in other Oxford dictionaries Definition of Diophantine equation in the British & World English dictionary