mersenneforum.org Auxiliary fractions observation
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2021-09-06, 10:16   #1
neskis

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
0.102225160401
The prepended remainders 0012214= 10510
AND
((40^6)-1)/399 = 105,025,641
*notice the 105 prepended to the repetend of 1/39.
(Also noted that 409510 = 3333334

I've worked out dozens of examples in many other bases and the same is always true. Another example is included in my photo.
Attached Files
 Mon, Sep 6, 2021, 10:07 AM.pdf (506.6 KB, 55 views)

 2021-09-09, 16:18 #2 Dr Sardonicus     Feb 2017 Nowhere 22×3×13×37 Posts Looks remarkably similar to the discussion in this thread.

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