Wednesday, January 1, 2020

elementary number theory - Find 11644mod645


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..


Find 11644mod645


enter image description here


Answer



Note that 645=3543. Then



11644(1)232213221(mod3) 1164416441(mod5) For the last modulus, we should determine the order of 11(mod43). To this end we first try 11q for qp1: 112358,1138112,117(8)2(2)1281. So with this 11644117461461(mod43) and so by the Chinese Remainder Theorem also 116441(mod645)


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...