1
$\begingroup$

We know that addition, subtraction and multiplication can be defined for integer modular arithmetic:

for $a \equiv b \mod n$ and $c \equiv d \mod n$, $a+c \equiv b+d \mod n$ and so on.

But is there any modular arithmetic property that relates $a \equiv b \mod m$ and $a \equiv c \mod mn$? Assume that every number here is an integer.

$\endgroup$
1
$\begingroup$

Consider that $a\equiv b (mod m)$ $\rightarrow$ a= b + lm and $a\equiv c (mod mn)$ $\rightarrow$ a= c + kmn . But then l= kn. What's this mean? Here's another hint: This result in number theory is sometimes called "casting out the moduls" or "reducing modulo m". What's this mean? Do you know?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.