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...

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, $1$ quotient...

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 operator.

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 \\mod (a + bi) $ …

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

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 think is …

Modular Arithmetic over a Matrix Ask Question Asked 13 years, 2 months ago Modified 8 years, 5 months ago

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 respects the …

Dec 4, 2025 · 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 $a-b$.

Feb 16, 2015 · From Stephen Abbott's - understanding analysis there is a section in the text which says: "The finite set $\\{0,1,2,3,4\\}$ is a field when addition and multiplication are computed modulo …