document.write( "Question 486936: Can you please help me? Can you give me answers to those problems and explain how to solve them? Thanks a lot!!!!
\n" ); document.write( "1. For each of the of the following parts, fi nd the inverse or explain why it does not exist.
\n" ); document.write( "(a) The inverse of 7 modulo 13.
\n" ); document.write( "(b) The inverse of 8 modulo 35.
\n" ); document.write( "(c) The inverse of 3 modulo 100.
\n" ); document.write( "(d) The inverse of 15 modulo 18.
\n" ); document.write( "(e) The inverse of 42 modulo 43.
\n" ); document.write( "2. Solve the following congruences:
\n" ); document.write( "(a) 7x == 8 (mod 13).
\n" ); document.write( "(b) 8x == 20 (mod 35).
\n" ); document.write( "(c) 3x == 75 (mod 100).
\n" ); document.write( "Thank you very much!!! \n" ); document.write( "
Algebra.Com's Answer #335275 by kunlex dy(1)\"\" \"About 
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 \n" ); document.write( "
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