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:

00: 00   Repeater: 101: 01   Repeater: 102: 02,04,08,16,32,64,28,56,12,24,48,96,92,84,68,36,72,44,88,76,52   Repeater: 2003: 03,09,27,81,43,29,87,61,83,49,47,41,23,69,07,21,63,89,67,01   Repeater: 2004: 04,16,64,56,24,96,84,36,44,76   Repeater: 1005: 05,25   Repeater: 106: 06,36,16,96   Repeater: 407: 07,49,43,01   Repeater: 408: 08,64,12,96,68,44,52,16,28,24,92,36,88,04,32,56,48,84,72,76   Repeater: 2009: 09,81,29,61,49,41,69,21,89,01   Repeater: 10\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}

#NumberTheory

Note by Lâm Lê
6 months, 4 weeks ago

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Comments

@Percy Jackson

Lâm Lê - 6 months, 4 weeks ago

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Nice :)

A Former Brilliant Member - 6 months, 4 weeks ago

@Frisk Dreemurr

Lâm Lê - 6 months, 4 weeks ago
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