1.Find the inverse of 7 modulo 13 (expressed as a residue between 0 and the modulus

2.Find the inverse of 8 modulo 35 (expressed as a residue between 0 and the modulus)

3.Find the inverse of 3 modulo 100 (expressed as a residue between 0 and the modulus)

4.Find the inverse of 15 modulo 18 (expressed as a residue between 0 and the modulus)

5.Find the inverse of 42 modulo 43 (expressed as a residue between 0 and the modulus)

Badada May 25, 2019

#1**+2 **

**%%time a = 7 m =13 def modInverse(a, m) : a = a % m for x in range(1, m) : if ((a * x) % m == 1) : return x print("The MMI = ", modInverse(a, m)):**

**1 - 7^(-1) mod 13 = 2 2 - 8^(-1) mod 35 = 22 3 - 3^(-1) mod 100= 67 4 - 15^(-1) mod 18= None [15 is not invertible modulo 18] 5 - 42^(-1) mod 43= 42**

Guest May 25, 2019

#2**+2 **

1. 7^(-1) (mod 13). Multiply both sides by two, such that when the result is divisible by thirteen the remainder is one. Thus, the answer is 2.3

2. We have 8^(-1) (mod 35), or 8*k is congruent to 1 (mod 35), and 8*22 is 176, which s 1 (mod 35), so 22 is the answer,

3. 3^(-1) (mod 100)m or 3*k is congruent to 1 (mod 100). Can you find the answer? Give it a try.

tertre May 25, 2019