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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