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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

357.0. "n divides a^n-b" by TOOLS::STAN () Thu Oct 17 1985 16:48

(Gerald Myerson)

Do there exist integers a,b other than a=2, b=1 such that if n divides
a^n-b, then n=1?  Ignore trivial cases.

A necessary condition on a,b is |a-b|=1.  This is not sufficient
since 2929|(3^2929-2).  The Lehmers have found the smallest n
that divides 2^n-3, namely n=4700063497.
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