For his Smith's Prize essay Mordell studied solutions of y2 = x3 + k, an equation which had been considered by Fermat . Thue had already proved a result which, combined with Mordell's work showed that this equation had only finitely many solutions but Mordell only learned about Thue 's work at a later date.
Para sa kanyang Smith's Prize sanaysay Mordell-aral ng mga solusyon ng y 2 = x 3 + k, kung saan nagkaroon ng isang equation na isinasaalang-alang sa pamamagitan ng Fermat. Thue had already proved isang resulta na, pinagsama sa Mordell ng trabaho ay nagpakita na ang equation na ito ay may lamang finitely maraming mga solusyon ngunit Mordell lamang natutunan tungkol sa Thue 's trabaho sa susunod na mga araw.