What is the 10th last digit of $17^{256}$?

Asked Jun 27 '20 at 04:17

Active Jun 27 '20 at 04:52

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What is the 10th digit of $17^{256}$ ?

I know how to do simpler version of this question (like finding the last digit or last two digits ) by writing the number in the form of $10m + n$ and then expanding using binomial theorem , but this approach is either too lengthy to apply here or not meant for this question. So could someone please help me solve this either by this approach in a doable way , or various different approaches are also highly appreciated.

Thanks!

edited Jun 27 '20 at 04:52

asked Jun 27 '20 at 04:17

ARROW

2

https://math.stackexchange.com/questions/619810/what-is-the-shortest-way-to-compute-the-last-3-digits-of-17256 – lab bhattacharjee Jun 27 '20 at 04:27
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Do you mean 10th last digit? $17^{256}=988379827\color{red}0\ldots\color{red}9784263681$ – Alexey Burdin Jun 27 '20 at 04:42
Yes , edited, thanks – ARROW Jun 27 '20 at 04:53
@lab bhattacharjee that worked , thanks ! – ARROW Jun 27 '20 at 04:57
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I think you are just meant to square eight times. You can reduce $\bmod 10^{10}$ along the way, but you need $20$ decimal digits in the square. My spreadsheet fails unless I make a high precision calculation. – Ross Millikan Jun 27 '20 at 05:01
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yeah right , I think the question isn't doable in a shorter way without a calculator , anyways I got the idea and different approaches , thanks ! – ARROW Jun 27 '20 at 05:14

What is the 10th last digit of $17^{256}$?

0 Answers0