2018年2月28日 · The result of 10 modulo 5 is 0 because the remainder of 10 / 5 is 0. The result of 7 modulo 5 is 2 because the remainder of 7 / 5 is 2. The reason your calculator says 113 modulo 120 = 113 is because 113 < 120, so it isn't doing any division. More generally, the idea is that two numbers are congruent if they are the same modulo a given number ...

2017年10月11日 · Is there a established notation for the remainder of integer division? For example, I want a function gives zero for non-negative even integers and one for non-negative odd integers. In computer c...

2022年6月16日 · I have been trying to find a formula for modulo for a long time now. I was wondering, is this even possible? I know there are lot's of solutions for this problem in computer science but is there a solution for this problem in arithmetics? I mean is there a function that uses only arithmetics actions that can solve this problem?

2024年12月3日 · One may also mean by the $\pmod{2}$ decoration that they are working in the ring of integers modulo 2, in which case 5 and 1 are not denoting integers, but equivalence classes modulo 2, in which case the two sides are literally equal. $5 = 1 \mod 2$ This is the same thing as the previous one, just typeset differently.

There are other versions of the modulo operator; some, return the "residue class of smallest absolute value" (for example, modulo $3$ will return either $-1$, $0$, or $1$, rather than $0$, $1$, or $2$; and modulo $7$ will return $-3$, $-2$, $-1$, $0$, $1$, $2$, or $3$).

As far as I know, I've never seen Absolute Value referred to as modulus, though wikipedia does acknowledge this use. Modulus and modulo both refer to the remainder operation. Generally speaking, "$5 \mod 7$" is read "$5$ modulo $7$," where the modulus is $7$. It's ultimately a matter of which you prefer to use.

7 div 5, 7 mod 5 versus -7 div -5, -7 mod -5 ends up with BOTH a different quotient as well as a different modulo. Ditto for -7 div 5, -7 mod 5 versus 7 div -5, 7 mod -5. Floored division is far more self consistent in that regard.

That lead me to wonder how one would deal with more complex problems involving modulo arithmetic. I know several rules for reducing equations involving all sorts of operators from simple addition up through very complex triple integrals and the like. But, I never learned any rules for manipulating the modulo operator.

2022年9月23日 · The moduli space is some sort of space of parameterizing space, modulo as in modular arithmetic and modulus as in the modulus of a complex number. Is there a reason all these words are the so similar?

2017年4月13日 · (I've come here from this question.) What's the difference between modulus and remainder? (Bearing in mind until 5 minutes ago I thought they were the same :P )