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What is the units digit of 17^381?

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What is the units digit of 17^381?

by Max@Math Revolution » Mon Jul 18, 2016 3:22 am
What is the units digit of 17^381?
A. 1
B. 3
C. 5
D. 7
E. 9

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by regor60 » Mon Jul 18, 2016 6:02 am
^2 = 9
^3 = 3
^4 = 1
^5= 7
^6 = 9

Repeats after 4.

How many packets of 4 in 381 ? > 95 remainder 1

E

Why did I start with 2 ? :roll:
Last edited by regor60 on Mon Jul 25, 2016 5:05 am, edited 1 time in total.
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by Max@Math Revolution » Sun Jul 24, 2016 1:38 am
From ~7^1=~7, ~7^2=9, ~7^3=~3, ~7^4=~1, the units digit is 7-->9-->3-->1-->7, and it repeats like this. Then from 17^381=17^(4(95)+1), we can see that the units digit is same as 17^1, which is 7.
The answer is, then, D.
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