# What is modular arithmetic used for?

## What is modular arithmetic used for?

Modular arithmetic is used extensively in pure mathematics, where it is a cornerstone of number theory. But it also has many practical applications. It is used to calculate checksums for international standard book numbers (ISBNs) and bank identifiers (Iban numbers) and to spot errors in them.

### How do you calculate modular?

How to calculate the modulo – an example

- Start by choosing the initial number (before performing the modulo operation).
- Choose the divisor.
- Divide one number by the other, rounding down: 250 / 24 = 10 .
- Multiply the divisor by the quotient.
- Subtract this number from your initial number (dividend).

**How do you reduce modular arithmetic?**

In modular arithmetic, when we say “reduced modulo ,” we mean whatever result we obtain, we divide it by n, and report only the smallest possible nonnegative residue. The next theorem is fundamental to modular arithmetic. Let n≥2 be a fixed integer. If a≡b (mod n) and c≡d (mod n), then a+c≡b+d(modn),ac≡bd(modn).

**What does a ≡ b mod n mean?**

Definition 3.1 If a and b are integers and n > 0, we write a ≡ b mod n to mean n|(b − a). We read this as “a is congruent to b modulo (or mod) n. For example, 29 ≡ 8 mod 7, and 60 ≡ 0 mod 15. n|(a − a) since 0 is divisible by any integer. Therefore a ≡ a mod n.

## Which is use for floor division?

The real floor division operator is “//”. It returns floor value for both integer and floating point arguments.

### Which algorithm is used for fast modular exponentiation calculation?

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 = d−e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m).

**What does mod 8 mean?**

Put simply, modulo is the math operation of finding the remainder when you divide two numbers together. If you are asking “what is 8 mod 8?” then what you really need to know is “what is the remainder when I divide 8 by 8?”.