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Recreations in the Theory of Numbers

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WHILE the author was a student, an enthusiastic mathematics professor recommended to the class a book entitled Mathematical Recreations and Essays, by W. W. R. Ball. The students dutifully made a note of the title and most of them no doubt promptly forgot about it. Many years later when the book was mentioned to several of the author's own classes, an unexpected hilarity invariably greeted the announcement of the title, and inquiry elicited the fact that "recreations" and "mathematics" were considered practically contradictory terms. If this was the response from a group of engineering students whose proficiency in mathematics was probably above average, what must be the attitude toward mathematics of the vast horde who take this subject by compulsion?

It was found, however, that mention of just a few "puzzle" problems immediately awakened the class from the proverbial student lethargy and that a problem connected with the theory of numbers aroused such enthusiastic response that the students were loath to return to their regular work. The stimulus of such problems permeated the class for a long time, and the prescribed work in algebra, trigonometry, analytic geometry, and calculus took on an added zest because of it. It was like a catalyst, which, although not itself taking part in a chemical reaction, excites other substances to do so.
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