After Christmas 2016!

What is the last digit of 122 6 2016 1226^{2016} ?

2 0 6 8 4

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2 solutions

Zach Abueg
Jan 2, 2017

Let's compute a few powers of 6 6 .

6 1 = 6 6^1 = \color{#D61F06}{6}

6 2 = 3 6 6^2 = 3\color{#D61F06}{6}

6 3 = 21 6 6^3 = 21\color{#D61F06}{6}

6 4 = 129 6 6^4 = 129\color{#D61F06}{6}

6 5 = 777 6 6^5 = 777\color{#D61F06}{6}

Any power of 6 6 , or number ending in 6 6 , will end in 6 6 .

Thus, 122 6 2016 1226^{2016} ends in 6 6 .

Good job for giving such a detailed and clear solution to this question! Way to go!

Jingyang Tan - 4 years, 4 months ago

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Am I supposed to take that as sarcastic?

Zach Abueg - 4 years, 4 months ago

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Of course not!!! Its really good!

Jingyang Tan - 4 years, 3 months ago

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@Jingyang Tan Oh haha, thank you!

Zach Abueg - 4 years, 3 months ago
Anubhav Pal
Jan 2, 2017

6^any number n belongs to natural no last digit is 6 then 1226^2016last digit is 6

An easy explanation for those people that are not so good at math! Good job!

Jingyang Tan - 4 years, 4 months ago

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