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Find the last six digits of \(5^{131313}\)

 Jul 26, 2018
 #1
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5^131313 =   70 498 418 681 817 ..................................... 942 169 189 453 125

 

=7.0498418................x 10^91,783

 Jul 26, 2018
 #2
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The general formula for this that would give the same last 6 digits as 5^131313 is:

5^(16n + 1), where n =1, 2, 3......etc. So, for n = 1, you have: 5^17=762,939,453,125. 

And since 131313 - 1 mod 16 =0, then 5^131313 = will also end in 453, 125.

 Jul 26, 2018

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