Saturday, 17 February 2018

modular arithmetic - What is 2632bmod12?




What is the correct answer to this expression:



2632(mod12)



When I tried in Wolfram Alpha the answer is 4, this is also my answer using Fermat's little theorem, but in a calculator the answer is different, 0.


Answer



First, note that 262(mod12), so 2632232(mod12).




Next, note that 24164(mod12), so 232(24)848(mod12), and 424(mod12).



Finally, 48(42)444(42)2424(mod12).



Then we get the result.



There are slicker solutions with just a few results from elementary number theory, but this is a very basic method which should be easy enough to follow.


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