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...

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...

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 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.

Mar 31, 2015 · Explore related questions modular-arithmetic See similar questions with these tags.

Explore related questions modular-arithmetic systems-of-equations linear-diophantine-equations See similar questions with these tags.

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 $8\\cdot 0=0$ and …

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 …

How do you reduce polynomials that are mod m? For example if I have 10x + 5 (mod 3) can I just reduce that to x + 2 (mod 3)?