# What is the inverse of mod 26?

## What is the inverse of mod 26?

Since 5^2 = -1 mod 26, then 5^4 = 1 mod 26, which is to say, that 5 * 5^3 = 1 mod 26. 5^3 is just 125. 125 % 26 = 21, so the multiplicative inverse in this case is 21.

What is the inverse of 19 Mod 26?

11*19 mod 26 = 1. While tricks like the above often work to compute inverses for small moduli, for larger moduli it is more efficient to use the extended Euclidean algorithm.

What is the inverse of 6 MOD 26?

Gcd(6, 26) = 2; 6 and 26 are not relatively prime. Therefore, 6 does not have a multiplicative inverse modulo 26. For, assume that it did; say, m is the multiplicative inverse of 6 modulo 26.

### What is the inverse of 7 mod 26?

15 is the inverse of 7 mod 26.

How do you solve Mod 26?

For each number in the plaintext, multiply it by a = 5, then add b = 17, and finally take the answer modulo 26. For example, to encrypt the plaintext letter ‘v’, which corresponds to 21, the calculation is: (5 × 21 + 17) mod 26 = 122 mod 26 ≡ 18.

What is the inverse of 11 Mod 26?

0.09090909090909
2 Answers. Java is technically correct, the inverse of 11 mod 26 is (approximately) 0.09090909090909 because 0.09090909090909 * 11 is approximately 1, whether mod 26 or not.

## What is the multiplicative inverse of 9 10?

-10/9
The multiplicative inverse of -9/10 is -10/9. To verify the answer, we will multiply -9/10 with its multiplicative inverse and check if the product is 1.

What is the multiplicative inverse of 3 mod 11?

4
The multiplicative inverse of “a modulo m” exists if and only if a and m are relatively prime (i.e., if gcd(a, m) = 1). Examples: Input: a = 3, m = 11 Output: 4 Since (4*3) mod 11 = 1, 4 is modulo inverse of 3(under 11).

Why is mod 26 in ciphers?

Using the modulo operator allows you to map every possible output of the matrix multiplication (encryption) to a letter in the alphabet ( 834 = 2 (mod 26) which is C), which lets you store the encrypted message in the form of a string of letters.

### What is the multiplicative inverse of 20?

The multiplicative inverse of a number is also called its reciprocal. The product of a number and its multiplicative inverse is equal to 1….Modular Multiplicative Inverse.

Type Multiplicative Inverse Example
Unit Fraction 1/x, x ≠ 0 x Multiplicative Inverse of 1/20 is 20

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