I completely understand the concept of modulus arithmetic and grasp all the main ideas. The only thing I don’t understand is equivalence classes. The formal definition is: Another interpretatio...

Dec 3, 2024 · This is fairly common to use when you need to move back and forth between integer and modular arithmetic. In particular, programming languages usually have such an …

I know how to solve mod using division i.e. $$11 \\mod 7 = 4$$ For this I did a simple division and took its remainder: i.e. $$11 = 7 \\cdot 1 + 4$$ Where $11$ was dividend, $7$ divisor, $1$ …

Jan 9, 2013 · I was wondering what would happen if we tried to do a modulo operand with complex numbers? For instance, what would be the answer (if any) to the next statement? $ x …

Sep 4, 2017 · My question is rather simple as I'm interested about modulus and multiplication, specifically whether it holds that $(a*b)\\,mod\\,n=(a\\,mod\\,n)*(b\\,mod\\,n)$?

The reason that equivalence class arithmetic proves smoother is that congruence mod m is not only an equivalence relation but is, additionally, an arithmetic congruence relation, i.e. it …

Dec 25, 2023 · Perhaps the best question to start with is " Can modular arithmetic be extended to the rational or real numbers?", which leads us to "What is modular arithmetic?", which I like to …

6 days ago · Modular arithmetic (clock arithmetic) is a system of integer arithmetic based on the congruence relation $a \equiv b \pmod {n}$ which means that $n$ divides $a-b$.

Jan 7, 2017 · However, I came across a question to do with modular arithmetic and I feel like it has a completely different meaning. Given a group $\mathbb {Z}/n\mathbb {Z}$, how do you …

Aug 15, 2018 · I had a doubt regarding the ‘mod’ operator So far I thought that modulus referred to the remainder, for example $8 \\mod 6 = 2$ The same way, $6 \\mod 8 = 6$, since $8\\cdot …