The method is most useful anywhere engineers or researchers need to pick sequence lengths, moduli, or generator parameters such that 2^A≡1 (mod p^t) conditions hold (or don’t). Used for PRNG design, scrambler alignment, transform sizing, or residue-field arithmetic. If you give me pairs of (p, t) I can give M instantly. If you are working on such selection parameters now using Hensel lifting or some other heuristic methods, or have in the past, that is/did take days to calculate, give me the pairs now and I can verify the results for you. Give me a challenge something you know should take days or weeks to calculate and verify. If you do give (p, t), (p, t), ... in this format so I can copy and paste it into my python script to run.