Speculations on some characteristic properties of numbers

arXiv0705.3929MaRDI QIDQ6205725

Publication date: 27 May 2007

Abstract: Translation of the Latin original "Speculationes circa quasdam insignes proprietates numerorum" (1784). E564 in the Enestrom index. In this paper Euler talks about Farey sequences and proves some results about the phi function, the number of positive integers less than and relatively prime to an integer. Euler uses the notation pi instead of phi.

Mathematics Subject Classification ID

History of mathematics in the 18th century (01A50) Arithmetic functions; related numbers; inversion formulas (11A25) Farey sequences; the sequences (1^k, 2^k, dots) (11B57)

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