I understand the concept of a Residual Number System and the concept of a Mixed Radix system, but I'm having difficulty getting any of the conversion methods I find to work in a simple case study.
I started at Knuth's Art of Computer Programming but that had a bit too much on the theory of the conversion, and once Euler was mentioned I was lost. Wikipedia has a nice section on the subject, which I tried here and here but both times I couldn't get back to the number where I started.
I found a good article here (PDF), which I condensed the relevant sections here, but I don't understand the multiplicative inverses and their notation. Specifically, how y_2 = |(3 - 19)|(1/31)|_7|_7 = |5 * 5|_7 Especially how |1/31|_7 = 5