# Last Digits of Powers (Under Construction)

Note: A red number means that the number appears, but doesn't repeat

## One Digit:

\begin{align} 0: & \ 0 & \ \ \text{ Repeater: }1 \\ 1: & \ 1 & \ \ \text{ Repeater: }1 \\ 2: & \ 2, 4, 8, 6 & \ \ \text{ Repeater: }4 \\ 3: & \ 3, 9, 7, 1 & \ \ \text{ Repeater: }4 \\ 4: & \ 4, 6 & \ \ \text{ Repeater: }2 \\ 5: & \ 5 & \ \ \text{ Repeater: }1 \\ 6: & \ 6 & \ \ \text{ Repeater: }1 \\ 7: & \ 7, 9, 3, 1 & \ \ \text{ Repeater: }4 \\ 8: & \ 8, 4, 2, 6 & \ \ \text{ Repeater: }4 \\ 9: & \ 9, 1 & \ \ \text{ Repeater: }2 \end{align}

## Two Digits:

\begin{aligned} 00: & \ 00 & \ \ \text{ Repeater: }1 \\ 01: & \ 01 & \ \ \text{ Repeater: }1 \\ 02: & \ \color{#D61F06}02\color{#333333}, 04, 08, 16, 32, 64, 28, 56,12,24,48,96,92,84,68,36,72,44,88,76,52 & \ \ \text{ Repeater: }20 \\ 03: & \ 03, 09, 27, 81, 43, 29, 87, 61, 83,49,47,41,23,69,07,21,63,89,67,01 & \ \ \text{ Repeater: }20 \\ 04: & \ 04, 16, 64, 56, 24,96,84,36,44,76 & \ \ \text{ Repeater: }10 \\ 05: & \ \color{#D61F06}05\color{#333333},25 & \ \ \text{ Repeater: }1 \\ 06: & \ 06,36,16,96 & \ \ \text{ Repeater: }4 \\ 07: & \ 07, 49, 43, 01 & \ \ \text{ Repeater: }4 \\ 08: & \ 08, 64, 12, 96,68,44,52,16,28,24,92,36,88,04,32,56,48,84,72,76 & \ \ \text{ Repeater: }20 \\ 09: & \ 09,81,29,61,49,41,69,21,89,01 & \ \ \text{ Repeater: }10 \end{aligned}

Note by Lâm Lê
2 weeks, 2 days ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

• bulleted
• list

1. numbered
2. list

1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

- 2 weeks, 2 days ago

Nice :)

- 2 weeks, 2 days ago