The Smallest Solution of \phi(30n+1)<\phi(30n) is ...
Abstract
It is known that there are infinitely many solutions to the inequality \phi(30n+1)<\phi(30n), where \phi is 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 \phi(30n+1)<\phi(30n), a number with 1116 digits.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1998
 DOI:
 10.48550/arXiv.math/9804025
 arXiv:
 arXiv:math/9804025
 Bibcode:
 1998math......4025M
 Keywords:

 Number Theory;
 11A25
 EPrint:
 3 pages, to appear in the Amer. Math. Monthly