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May 14th, 2018, 06:39 AM   #11
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Quote:
Originally Posted by Micrm@ss View Post
Euler's theorem. Which you apparently either didn't apply or didn't mention.
It states that if $a$ is not divisible by $2$ or $5$, then the last digit of $a^4 = 1$.
Thus for example, to compute
$$333^{4323133}$$
we write $4323133 = 4*1080783 + 1$
Hence in mod 10
$$333^{4323133} = (333^4)^{1080783}333 = 333 = 3.$$
Isn't this a lot easier?????

Now if $a$ is divisible by $5$, then the last digit of $a$ is always $5$ or $0$, and it is easy to see which.
If $a$ is divisible by $2$, then use that the last digit of $2^5 = 2$.


This is the same thing explained in this video but in a better way
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May 14th, 2018, 08:07 AM   #12
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Define "better way".
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May 14th, 2018, 09:27 AM   #13
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Quote:
Originally Posted by davidJ View Post
This is the same thing explained in this video but in a better way
Sure except that you make it appear like a magic trick, while I explain why it works.
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