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the last digit in expansion of 17^256 is

Guest Feb 21, 2015

Best Answer 

 #1
avatar+92788 
+5

Notice the pattern generated by raising a number ending in 7 to the following powers.....

7^1 = 7      7^2 = 49    7^3 = 343    7^4 = 2401 

And this cyclic pattern repeats every four powers

So    ...   256/4 = 64

And this whole number tells us that 7^256 completes a cycle of 4, so this number ends in a "1"

 

CPhill  Feb 21, 2015
 #1
avatar+92788 
+5
Best Answer

Notice the pattern generated by raising a number ending in 7 to the following powers.....

7^1 = 7      7^2 = 49    7^3 = 343    7^4 = 2401 

And this cyclic pattern repeats every four powers

So    ...   256/4 = 64

And this whole number tells us that 7^256 completes a cycle of 4, so this number ends in a "1"

 

CPhill  Feb 21, 2015

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