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The Smallest Solution of ϕ(30n+1)<ϕ(30n) is ...

Greg Martin
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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.

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Greg Martin. 1998-04-06. The Smallest Solution of ϕ(30n+1)<ϕ(30n) is .... https://arxiv.org/abs/math/9804025

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