I understand through trial and error that d=91, but trial and error is extremely inefficient and slow. I understand that you can use the extended Euclidean Algorithm to find d faster, but I'm encountering some unexpected problem. For some reason, I'm unable to move past the first step, could someone point out what I'm missing.
19d $\equiv$ 1 (mod 96)
96 = 5*19 + 1
$1 = 96 - 5\times19 = 3\times2^5 - 5\times19$