The fifth power of any one-digit number ends with that number:

0⁵ = 0
1⁵ = 1
2⁵ = 32
3⁵ = 243
4⁵ = 1024
5⁵ = 3125
6⁵ = 7776
7⁵ = 16807
8⁵ = 32768
9⁵ = 59049

11/26/2016: UPDATE, after hearing from some readers who are thinking more deeply than I am:

First, this immediately implies that any integer raised to the fifth power ends with the same digit as the original number.

Second, the same effect occurs regularly at higher powers, specifically 9, 13, 17, and x = 1 + 4n where n = {0, 1, 2, 3, …}.

Does anyone know what this rule is called? I found it in Reuben Hersh and Vera John-Steiner’s 2011 book Loving + Hating Mathematics — Eugene Wigner writes of falling in love with numbers at his school in Budapest: “After a few years in the gymnasium I noticed what mathematicians call the Rule of Fifth Powers: That the fifth power of any one-digit number ends with that same number. Thus, 2 to the fifth power is 32, 3 to the fifth power is 243, and so on. At first I had no idea that this phenomenon was called the Rule of Fifth Powers; nor could I see why it should be true. But I saw that it was true, and I was enchanted.”

I actually can’t find a rule by that name. Perhaps it goes by a different name in English-speaking countries?

12/08/2016 UPDATE: It’s a consequence of Fermat’s little theorem, as explained in this extraordinarily helpful PDF by reader Stijn van Dongen.

(Thanks to Evan, Dave, Sid, and Stijn.)