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Mathematical Treasure: Lucas’s Theory of Numbers

Frank J. Swetz (The Pennsylvania State University)

Edouard Lucas (1842-1891) was a French mathematician and a number theorist. In his work, he investigated the properties of the Fibonacci sequence and devised a related number sequence that bears his name, “Lucas numbers.” In 1891, he published Volume I of Théorie des Nombres; the second volume never appeared.

In the “Preface,” Lucas reviewed developments in modern number theory.

“Multiplication curiosities” are shown on page 28.                           

Appropriate problems and exercises are distributed throughout the text. Here on page 51, it is shown that 232 – 1 is divisible by 641.


The images above were supplied through the cooperation of the Pennsylvania State University Libraries.

Index to Mathematical Treasures


Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Lucas’s Theory of Numbers," Convergence (June 2017)