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Unit digit of 7^7777?

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by papgust » Tue Feb 02, 2010 9:38 pm
You know that 7^x repeats unit digits every fourth index.

7^1 = 7
7^2 = 9
7^3 = 3
7^4 = 1
7^5 = 7 (Again)
..
..

Now take the power 7777 and mod it by 4 (As it repeats every fourth index)

7777 % 4 = 1. Remainder is 1.

Raise the base 7 to the power 1 i.e. remainder. 7^1 = 7

So, units digit of 7^7777 = 7
Last edited by papgust on Tue Feb 02, 2010 11:07 pm, edited 1 time in total.
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by fibbonnaci » Tue Feb 02, 2010 10:45 pm
papgust wrote:

So, units digit of 7^7777 = 1
Papgust, i guess u meant to say units digit of 7^7777 = 7
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by papgust » Tue Feb 02, 2010 11:06 pm
Yup :) Sorry, a typo.
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