Can someone just explain to me the basic process of what is going on here? I understand everything until we start adding 1's then after that it all goes to hell. I just need some guidance. The Problem with the solution is attached.
Thanks in advance..
Answer
Note that 645=3⋅5⋅43. Then
11644≡(−1)2⋅322≡1322≡1(mod3) 11644≡1644≡1(mod5) For the last modulus, we should determine the order of 11(mod43). To this end we first try 11q for q∣p−1: 112≡35≡−8,113≡−8⋅11≡−2,117≡(−8)2⋅(−2)≡−128≡1. So with this 11644≡117⋅46≡146≡1(mod43) and so by the Chinese Remainder Theorem also 11644≡1(mod645)
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