My Math Forum Short Trick Number System

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May 14th, 2018, 07:39 AM   #11
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Quote:
 Originally Posted by Micrm@ss 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

 May 14th, 2018, 09:07 AM #12 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,486 Thanks: 950 Define "better way".
May 14th, 2018, 10:27 AM   #13
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Quote:
 Originally Posted by davidJ 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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