How does the modulo operator work in Python?

The Python modulo operator calculates the remainder of dividing two values. This operator is represented by the percentage sign (%). The syntax for the modulo operator is: number1 % number2. The first number is divided by the second then the remainder is returned.

What is modulo operator give an example?

The Modulus is the remainder of the euclidean division of one number by another. % is called the modulo operation. For instance, 9 divided by 4 equals 2 but it remains 1 . Here, 9 / 4 = 2 and 9 % 4 = 1 .

How is modulo calculated?

Modulus on a Standard Calculator
  • Divide a by n.
  • Subtract the whole part of the resulting quantity.
  • Multiply by n to obtain the modulus.

How does modulo work with negative numbers?

The modulo operator returns the remainder of a division. Doing an integer division and then multiplying it again means finding the biggest number smaller than a that is dividable by n without a remainder. … Subtracting this from a yields the remainder of the division and by that the modulo.

Is modulo distributive over addition?

Addition and multiplication is association under modulos. One way to see this is to note that a≡b (mod n) means that a and b have the same remainder when dividing by n.

Which operators are known as modulo operator?

The modulo operator, denoted by %, is an arithmetic operator. The modulo division operator produces the remainder of an integer division. produces the remainder when x is divided by y.

What modulo means?

The modulo (or “modulus” or “mod”) is the remainder after dividing one number by another. Example: 100 mod 9 equals 1. Because 100/9 = 11 with a remainder of 1. Another example: 14 mod 12 equals 2.

Is modulo additive?

The additive group of integers modulo m (Zm,+m) is the set of integers modulo m under the operation of addition modulo m.

Is modulo a mathematical operator?

The modulus operator – or more precisely, the modulo operation – is a way to determine the remainder of a division operation. Instead of returning the result of the division, the modulo operation returns the whole number remainder.

How do you distribute modulo?

A few distributive properties of modulo are as follows:
  1. ( a + b) % c = ( ( a % c ) + ( b % c ) ) % c.
  2. ( a * b) % c = ( ( a % c ) * ( b % c ) ) % c.
  3. ( a – b) % c = ( ( a % c ) – ( b % c ) ) % c.
  4. ( a / b ) % c = ( ( a % c ) / ( b % c ) ) % c.

Can modulo multiply?

Modular multiplication is pretty straightforward. It works just like modular addition. You just multiply the two numbers and then calculate the standard name. For example, say the modulus is 7.

What is modulo art in math?

Modulo Art is the Art of Mathematics and Design. It uses number pattern formed by Modular Arithmetic to create a unique and artistically pleasing designs.

How do you do modulo subtraction?

How is modular arithmetic used in cryptology?

One major reason is that modular arithmetic allows us to easily create groups, rings and fields which are fundamental building blocks of most modern public-key cryptosystems. For example, Diffie-Hellman uses the multiplicative group of integers modulo a prime p.

How do you teach modular arithmetic?

The best way to introduce modular arithmetic is to think of the face of a clock. The numbers go from 1 to 12, but when you get to “13 o’clock”, it actually becomes 1 o’clock again (think of how the 24 hour clock numbering works). So 13 becomes 1, 14 becomes 2, and so on.

What is modulo inverse of a number?

A modular inverse of an integer (modulo ) is the integer such that. A modular inverse can be computed in the Wolfram Language using PowerMod[b, -1, m]. Every nonzero integer has an inverse (modulo ) for a prime and not a multiple of. . For example, the modular inverses of 1, 2, 3, and 4 (mod 5) are 1, 3, 2, and 4.

How do you calculate modulo congruence?

A simple consequence is this: Any number is congruent mod n to its remainder when divided by n. For if a = nq + r, the above result shows that a ≡ r mod n. Thus for example, 23 ≡ 2 mod 7 and 103 ≡ 3 mod 10. For this reason, the remainder of a number a when divided by n is called a mod n.

What do you understand by symmetric key cryptography?

Symmetric Key Cryptography also known as Symmetric Encryption is when a secret key is leveraged for both encryption and decryption functions. This method is the opposite of Asymmetric Encryption where one key is used to encrypt and another is used to decrypt.

What properties of the modular arithmetic can be exploited for efficient computation of modular exponentiation?

Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = be mod m = de mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation is efficient to compute, even for very large integers.