Open AccessON TWO INTERESTING PROPERTIES OF PRIMES, P, WITH RECIPROCALS IN BASE 10 HAVING MAXIMUM PERIOD P-1.
Author(s) -
K. Subramani
Publication year - 2020
Publication title -
journal of mathematical sciences and computational mathematics
Language(s) - English
Resource type - Journals
eISSN - 2688-8300
pISSN - 2644-3368
DOI - 10.15864/jmscm.1204
Subject(s) - decimal , mathematics , magic square , arithmetic , base (topology) , period (music) , magic (telescope) , discrete mathematics , combinatorics , mathematical analysis , physics , quantum mechanics , acoustics
In this note we have studied some properties of decimal digits obtained by dividing 1 by primes which have maximum period property, namely, inverses of primes, p, whose decimal representation repeats after p-1. For such primes up to 1000, we have given a method for finding decimal digits of their inverses without using division. This works for many non-primes also. We have also given a construction method for obtaining magic squares for primes, 17, 29, 61 and 97 for which such magic squares are not known.