Thursday, 2 November 2017

elementary number theory - Working out modulo without a calculator



How does one determine modulo without a calculator in cases like this:
157135(mod14)

Normally I would simply divide what is given by the modulo number and take the decimal output and times it by the modulo number. How can I work out 157135(mod14) without the use of a calculator?



Now what I am thinking is:
151mod14
1571mod14
131mod14
1321mod14
1351mod14
[157135(mod14)]=1(mod14)+1(mod14)=2mod14
Is that right?



Answer



Yes, that's correct! [157135](mod14)=2(mod14)


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