Almost Automorphic Number
Number Theory
Level
5
\[\Large 249^3 = 15438\underline{249}\]
An automorphic number is defined as a positive integer \(n\) such that the trailing digits of \(n^m\), where \(m\) is a positive integer, is \(n\) itself.
Let us define an almost automorphic number as a number where \(n\) only appears as the trailing digits of \(n^m\) when \(m\) is odd. How many almost automorphic numbers are less than 1000?
by
Garrett Clarke