The Smallest Solution of ϕ(30n+1)<ϕ(30n) is ...
Greg Martin
Abstract
It is known that there are infinitely many solutions to the inequality ϕ(30n+1)<ϕ(30n), where ϕis the familiar Euler totient function. However, there are no solutions with n<20,000,000, and computing a solution would seem to involve factoring integers with hundreds of digits. In this note, we describe how to get around the need to factor such large integers in addressing inequalities of this type, and we explicitly compute the smallest solution n of ϕ(30n+1)<ϕ(30n), a number with 1116 digits.
Create a lesson
Related papers
An ergodic approach to equations of the form x+y=α(n)
Vitaly Bergelson, Hao Pan, Saúl Rodríguez Martín
Rogers--Ramanujan identities from the geometry of Xa=Yb
Yifeng Huang, Kenny Lau, Ken Ono
Computational results on sums of a prime with squares or cubes
Kenny Applegate, Kyle Pratt
Finding New Limit Points of Mahler Measure by Methods of Missing Data Restoration
Jean-Marc Sac-Épée, Souad El Otmani, Armand Maul et al.
Low moments of automorphic random multiplicative function sums
Sun-Kai Leung
A problem of Yang and Chen on weighted representation functions
Shuang-Shuang Li, Ya-Ting Xu, Xiao-Hui Yan