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Modulus operator gives you the result in 'reduced residue system'. For example for mod 5 there are 5 integers counted: 0,1,2,3,4. In fact 19=12=5=-2=-9 (mod 7). The main difference that the answer is given by programming languages by 'reduced residue system'.
What's the difference between “mod” and “remainder”? C does not define a "mod" nor "modulo" operator/function, such as the integer modulus function used in Euclidean division or other modulo. C defines remainder. Let us compare "remainder" per the % operator to the Euclidean "mod". "Euclidean mod" differs from C's a%b operation when a ...
How often does that happen? Exactly 6 lines apart (excercise : write numbers 1..30 and underline the ones that satisfy this condition), starting at 6-th line (count = 5). To get desired behaviour from your code, you should change condition to count % 5 == 4, what will give you newline every 5 lines, starting at 5-th line (count = 4).
16/5= 3 Remainder 1 i.e 16 Mod 5 is 1. 0/5= 0 Remainder 0 i.e 0 Mod 5 is 0. -14/5= 3 Remainder 1 i.e. -14 Mod 5 is 1. See Khan Academy Article for more information. In Computer science, Hash table uses Mod operator to store the element where A will be the values after hashing, B will be the table size and R is the number of slots or key where ...
But modulus does not work that way. It ignores the decimal quotient value or ratio returned from division, takes the quotient expression of "0 with a remainder of 1" in 1/3 , and extracts the 1 or remainder that was returned from that division.
Basically in R with x = 2 and y = - 5, x mod y = -3; or using definition x = k*q + r we have r = x - k*q = -3. Still, this is kind of quirky in a mathematical sense because "integer part product" ( k*q ) actually exceeds the dividend ( x ), thus defining the remainder ( r ) as a negative integer...
The difference between mod and rem is subtle, but important. (-1 mod 2) would normally give 1. More specifically given two integers, X and Y, the operation (X mod Y) tends to return a value in the range [0, Y). Said differently, the modulus of X and Y is always greater than or equal to zero, and less than Y.
Note that there is also a function for this operator in the standard library operator.mod (and the alias operator.__mod__): >>> import operator >>> operator.mod(5, 2) # equivalent to 5 % 2 1 But there is also the augmented assignment %= which assigns the result back to the variable:
For your specific case, x ≡ 1 (mod N) can be represented as x % N === 1 in JavaScript if x is never negative. Otherwise, your equality will not hold even though it should: for example, -1 ≡ 1 (mod 2) but (-1) % 2 === -1, which isn't equal to 1 even though they're "equal" in the modular arithmetic sense.
The X here means that we're working with polynomials. Mod X^r - 1 means that we mod all of the polynomial exponents by r. Mod n means that we mod all of the coefficients by n. As an example, if we have a polynomial X^4 + 4 X^3 + 6 X^2 + 4 X + 1 and we're modding by X^3 - 1 (i.e., r = 3) and n = 5, then we get