When students engage with a digital tool to tackle a mathematical task, the interplay between their digital competencies and mathematical abilities gives rise to what is termed mathematical digital competency (MDC). Recognising the significance of MDC as an integral component for contemporary students, the relevance of cultivating mathematical digital competency for teaching (MDCT) becomes apparent. We posit that for teachers to effectively guide students in the development of their MDC, possessing MDCT is imperative. In this paper, drawing upon the theoretical frameworks of instrumental orchestration, the documentational approach to didactics, and the Danish competencies framework's six didactico-pedagogical competencies of mathematics teachers, we propose a theoretical conceptualization of teachers' mathematical and digital competencies in the context of teaching mathematics with technology. Expanding upon the preliminary definition of students' MDC, we incorporate pedagogic, theoretical elements tailored to teachers, encapsulating it as MDCT. To expound on the various facets of MDCT, we provide an illustrative example featuring a mathematics teacher proficient in the utilisation of digital technologies and programming.