Find the last six digits of \(5^{131313}\)
5^131313 = 70 498 418 681 817 ..................................... 942 169 189 453 125
=7.0498418................x 10^91,783
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.
