Sage-Tips

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.

How do you find the inverse of a modulo?

A naive method of finding a modular inverse for A (mod C) is:

1. Calculate A * B mod C for B values 0 through C-1.
2. The modular inverse of A mod C is the B value that makes A * B mod C = 1. Note that the term B mod C can only have an integer value 0 through C-1, so testing larger values for B is redundant.

What is the inverse of 7 mod 11?

7x≡1≡12≡23≡34≡45≡56(mod11). Then from 7x≡56(mod11), we can cancel 7, obtaining x≡8(mod11). Hence, −3 is the inverse of 7(mod11).

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’s the inverse of 7?

Here, 1⁄7 is called the multiplicative inverse of 7. Similarly, the multiplicative inverse of 13 is 1⁄13. Another word for multiplicative inverse is ‘reciprocal’.

How do you find the reciprocal of a modulo 26?

For an integer x, its multiplicative inverse modulo n (if one exists), denoted x−1, is the number such that x × x−1 ≡ 1 modulo n. For example, the multiplicative inverse of 5 modulo 26 is 21, because 5 × 21 ≡ 1 modulo 26 (because 5 × 21 = 105 = 4 × 26 + 1 ≡ 1 modulo 26).

What is the sum of 7 and its additive inverse?

ZERO
The sum of 7 and its opposite (-7) is ZERO. Property: For every number a, there is a number -a so that a + (-a) = 0 and (-a) + a= 0. The additive inverse of a number is a number such that the sum of the two numbers is 0.

What is the additive inverse of 7 *?

Add 7 to both sides: x = 7 is the additive inverse.

What is the multiplicative inverse of 7 modulo 26?

Therefore 26 times 4 will be one less than a multiple of 7, and 26 times 4 is 104. So 105 is a multiple of 7 which is one more than a multiple of 26. And 105 is 7 times 15. Therefore 15 is the multiplicative inverse of 7 modulo 26.

What is the remainder of 5 modulo 7?

First note that 26 is congruent to 5 modulo 7, that is, when you divide 26 by 7 you get a remainder of 5. Next 5 times 4 is 20, which is one less than a multiple of 7. Ther There are several good answers already, but here’s another way to approach the problem.

Is 26 times 4 a multiple of 7?

First note that 26 is congruent to 5 modulo 7, that is, when you divide 26 by 7 you get a remainder of 5. Next 5 times 4 is 20, which is one less than a multiple of 7. Therefore 26 times 4 will be one less than a multiple of 7, and 26 times 4 is 104. So 105 is a multiple of 7 which is one more than a multiple of 26.