Definition of Diophantine equation in English:

Share this entry

Diophantine equation

Pronunciation: /ˌdīəˈfanˌtin/ Pronunciation: /-tīn/


A polynomial equation with integral coefficients for which integral solutions are required.
Example sentences
  • That conjecture offers a new way of expressing Diophantine problems, in effect translating an infinite number of Diophantine equations (including the equation of Fermat's last theorem) into a single mathematical statement.
  • Instead of asking whether a given Diophantine equation has a solution, ask ‘for what equations do known methods yield the answer?’
  • Wolfram displays a table of some of the simplest possible Diophantine equations, distinguishing between those known to have integer solutions, those known to have no integer solutions, and those for which the question is still open.


Early 18th century: named after Diophantus.

For editors and proofreaders

Syllabification: Di·o·phan·tine e·qua·tion

Share this entry

What do you find interesting about this word or phrase?

Comments that don't adhere to our Community Guidelines may be moderated or removed.