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Old 2021-08-09, 11:09   #1317
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"Garambois Jean-Luc"
Oct 2011

2×3×7×17 Posts

I just want to ask two questions about the demonstrations of the conjectures stated around this project.

1) I am totally unable to do it myself, but wouldn't it be possible to prove conjecture (10) by a method similar to the one used for conjecture (2) ? (see henryzz's post #476 and warachwe's post #480).
Indeed, 2^12-1 = 3^2*5*7*13 and we do have the 13 which preserves the 7 for the second iteration, except perhaps for some values of k that I did not examine, but the whole problem is precisely there, isn't it ?

2) At the end of the quote below, Alexander says: "(the composite ones will be harder)".
But does this mean that no one knows how to do such demonstrations yet, or does it just mean that we know how to do them, but that it is very long and tedious ?

Originally Posted by Happy5214 View Post
I updated the conjectures page to add some of the more trivial proofs. Specifically, I added proofs for index 1 conjectures for bases 2, 3, and 5, which all use algebraic factors. You could probably use that template and FactorDB to fill in the rest of the index 1 conjecture proofs for the remaining prime bases (the composite ones will be harder).
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