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Answer for the clue "Study of integers and their properties ", 13 letters:
number theory

Word definitions for number theory in dictionaries

Wiktionary Word definitions in Wiktionary
n. (context mathematics English) The branch of pure mathematics concerned with the properties of integers.

Wikipedia Word definitions in Wikipedia
Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers . It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime ...