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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)

 May 25, 2019
 #1
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%%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

 May 25, 2019
 #2
avatar+4249 
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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. 

 May 25, 2019
 #3
avatar+101733 
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Babada, you do not need people to do all your homework for you. (Unless you are just bone lazy that is)

Just ask one question, learn from the answer and try doing the others for yourself!

 May 26, 2019

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