SOLUTION: Can you please help me? Can you give me answers to those problems and explain how to solve them? Thanks a lot!!!! 1. For each of the of the following parts, fi nd the inverse or e

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Question 486936: Can you please help me? Can you give me answers to those problems and explain how to solve them? Thanks a lot!!!!
1. For each of the of the following parts, fi nd the inverse or explain why it does not exist.
(a) The inverse of 7 modulo 13.
(b) The inverse of 8 modulo 35.
(c) The inverse of 3 modulo 100.
(d) The inverse of 15 modulo 18.
(e) The inverse of 42 modulo 43.
2. Solve the following congruences:
(a) 7x == 8 (mod 13).
(b) 8x == 20 (mod 35).
(c) 3x == 75 (mod 100).
Thank you very much!!!
Answer by kunlex dy(1) About Me  (Show Source):
You can put this solution on YOUR website!
In a question like this you need to be specific while talking about inverses it might be additive inverses or multiplicative inverses. But I will try to explain while multiplicative inverses does not exist in some cases. the identity element is 1. consider 2x7, you will get 14 which under modulo 13 gives 1 hence 2 is the inverse of7. consider 22x8 which gives 176 and so 1 under modulo 1 so, 22 is the inverse of 8 under modulo 35. Also consider 67x3 which also gives 1 under modulo 100. The inverse actually exist only if the number and the modulo are relatively prime i.e no commom factors consider 15mod18, 15 and 18 has 3 as a common factor so 15 can never have any inverse under mod 18. Try the remaining then I will see to them if you can't handle them