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Forum URL: http://www.cut-the-knot.org/cgi-bin/dcforum/forumctk.cgi
Forum Name: Middle school
Topic ID: 130
Message ID: 4
#4, RE: Fifth Power Of Digits
Posted by alexb on Feb-23-08 at 04:46 PM
In response to message #2
>1. Why after one, five is the first digit with this
>property?

Because 10 = 2*5 and 2 is too small.

>2. Why other one, only 5 and 6 hold the property: the last
>digit of x^n is the same x with any n?


Base 
6
3² = 13

4² = 24
10
5² = 25

6² = 36
12
4² = 14

9² = 69
14
7² = 37

8² = 48
15
6² = 26

A² = 6A
18
9² = 49

A² = 5A
21
7² = 27