Modular Multiplicative Inverse
Hi I do not understand the idea of Modular Multiplicative Inverse at all. I have tried reading up on modular arithmetic for a day, but I still do not understand it.
I had the following question, which is a past olympiad question:
N is a 4 digit number wich doesnt end in a 0, and R(N) is a 4 digit integer obtained by reversing the digits of N. So R(1997) = 7991
Determine all such integers N for which R(N) = 4N + 3.
The answer is 1997 only. Below is the solution:
N = 1000a + 100b + 10c + d
Since R(N) is odd, a is odd. Also, 4N + 3 is 4 digits so a<3.
R(N) = 4N + 3
1000d + 100c + 10b + 1 = 4000 + 400b + 40c + 4d + 3
"now working modulo 5, we see 4d=3(mod 5) so d=2(mod 5)."
I dont understand where this comes from... The equals signs here actually should be 3 lines, so ignore that.
So d = 2 or d = 7 etc..