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Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.
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- Mathematics is the queen of the sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
- Carl Friedrich Gauss, in Gauss zum Gedächtniss (1856) by Wolfgang Sartorius von Waltershausen, as translated in Memorabilia Mathematica; or, The Philomath's Quotation-Book (1914) by Robert Édouard Moritz, p. 271
- Most texts on number theory contain inserted historical notes but in this course I have attempted to obtain a presentation of the results of the theory integrated more fully in the historical and cultural framework. Number theory seems particularly suited to this form of exposition, and in my experience it has contributed much to making the subject more informative as well as more palatable to the students. ...for the understanding of a greater part of the subject matter a knowledge of the simplest algebraic rules should be sufficient.
- Oystein Ore, Number Theory and its History (1948)
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