Wednesday, 6 March 2013

modular arithmetic - basic modulus question



So if so a \equiv b \pmod{n}, which should be read as "a is congruent to b modulo n" which from what I understand is something among the lines of "a is the remainder when b is divided by n".



Now, given 51 \equiv 41 \pmod{5} means the remainder of 41 divided by 5 is 1, so this is a? I am confused as a looks to be 51?



Answer



41 \pmod 5 \equiv1\pmod5 (This is \frac{41}{5}, with a remainder of 1.)



51 \pmod 5 \equiv1\pmod5 (This is \frac{51}{5}, also with a remainder of 1.)



Therefore: 41\equiv 51 \pmod 5.



a\equiv1\pmod5



b\equiv1\pmod5



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