Table of Contents

## What is the multiplicative inverse of 5 in modulo 7 arithmetic?

Since \(5\cdot 3 \equiv 1 \pmod{7}\text{,}\) we say that \(3\) is a multiplicative inverse of 5 modulo 7. Similarly, 5 is a multiplicative inverse of 3 modulo 7.

**What is the additive inverse of 2 in Z7?**

If we examine Z/7, we find that every element there does have an additive inverse. For example, for the element 2, we find the additive inverse to be 5, as 2+5=0 (computed modulo 7).

**What is the multiplicative inverse of 7 in z10?**

A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1. For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1!

### What is the inverse of 4 modulo 5?

. For example, the modular inverses of 1, 2, 3, and 4 (mod 5) are 1, 3, 2, and 4.

**What inverse 5?**

The multiplicative inverse of 5 is 1/5.

**How do you find the reciprocal 5 7?**

The reciprocal of 57 is 75 .

## What is the multiplicative inverse of 5 by 8?

Therefore the multiplicative inverse of 5/8 is 8/5.

**What is the multiplicative inverse of 4?**

1/4

The multiplicative inverse of 4 is 1/4. (One-fourth is 1/4 in written form.)

**How do you find the inverse of 5?**

For example, the reciprocal of 5 is 1/5. Place a decimal number as the denominator of a fraction with 1 as the numerator, then divide to calculate the reciprocal of a decimal. For example, the reciprocal of 0.5 is 1/0.5. Dividing 1 by 0.5 is the same as dividing 10 by 5, so 1/0.5 also equals 2.

### What is the multiplicative inverse of 5?

For example, the multiplicative inverse of 5 is 1/5. The product of a number and its multiplicative inverse is 1. For example, consider the number 13. The multiplicative inverse of 13 is 1/13.

**What is the remainder of Z7 if Z7 is 5?**

When we define the elements Z7 we define a group so every element, including 5, has a multiplicative inverse. So multiply each until you get a 1 (as a remainder). 0*5=0, 1+5=5, 3*5 = 15 which is 1, mod 7. Check by dividing 15 by 7 and the remainder is 1.

**What is the multiplicative inverse of 6 and mod 13?**

Any number times it’s inverse equals 1. (6×11)mod13~1. The additive inverse of a number plus the number equals 0. So (6+7)mod13~0 so 11 is a multiplicative inverse of 6, mod13 and 7 is an additive is inverse of 6, mod 13.

## How do you find the modular multiplicative inverse of an integer?

Method 1: For the given two integers say ‘a’ and ‘m’, find the modular multiplicative inverse of ‘a’ under modulo ‘m’. The modular multiplicative inverse of an integer ‘x’ such that. ax ≡ 1 ( mod m ) The value of x should be in the range of {0, 1, 2, … m-1}, i.e., it should be in the ring of integer modulo m.