2007/05/27 by Leonhard Euler, Euler, Leonhard
Mathematics · #History and Theory of Mathematics #Mathematics and Applications #math.HO #math.NT #msc:01A50 #msc:11A25 #msc:11B57
paper · pdf · doi:10.48550/arxiv.0705.3929
9 pages
arxiv created 2007/05/27 · arxiv updated 2009/12/01
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.