20210906, 10:16  #1 
Feb 2019
17 Posts 
Auxiliary fractions observation
I was watching a vedic math YouTube video on the concept of auxiliary fractions and noticed something about the prepended remainders. I am not well educated in mathematics and lack the proper terminology, so I have attached a photo. I'll do my best to explain an example and welcome any insight. Most likely a well known concept, but I'd like to learn more!
Ex: 1/39 = Auxiliary fraction first order 0.1/4 0._{1}0_{2}2_{2}5_{1}6_{0}4_{0}1 The prepended remainders 001221_{4}= 105_{10} AND ((40^6)1)/399 = 105,025,641 *notice the 105 prepended to the repetend of 1/39. (Also noted that 4095_{10} = 333333_{4} I've worked out dozens of examples in many other bases and the same is always true. Another example is included in my photo. 
20210909, 16:18  #2 
Feb 2017
Nowhere
2^{2}×3×13×37 Posts 
Looks remarkably similar to the discussion in this thread.

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