Proving the equation

RobboMather

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Nov 18, 2020
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Hi, I'm writing the work in which I change some hard-to-prove conjecture into easier-to-prove, but not easy, conjecture that is below. Unfortunately, I've got a problem with this one. If somebody had an idea, hint or wanted to do it, I'd be grateful. 20201118_120809_HDR.jpg
 
1) I was wondering if it actually means anything.
2) It looks like a problem for Russell and Whitehead.
3) Why are you looking at this if you have nothing to go on?
4) If you have something to go on, why didn't you share it with us?
 
1) I was wondering if it actually means anything.
2) It looks like a problem for Russell and Whitehead.
3) Why are you looking at this if you have nothing to go on?
4) If you have something to go on, why didn't you share it with us?
1) Ok, it might be unclear. Here is thesis word by word: For all natural number [MATH]n[/MATH], where [MATH]n \in \{1,2,3,...\}[/MATH], we can find the sequence of natural numbers [MATH](a_m)[/MATH], whose length is equal to [MATH]m[/MATH], such that [MATH]a_1\in \{0,1,2,...\}[/MATH] and [MATH]\forall (i \in [2,m])[/MATH] [MATH]a_i\in \{1,2,3,...\}[/MATH] and also we can find number [MATH]k[/MATH], where [MATH]k \in \{1,2,3,..\}[/MATH]. Everything is in this relation: [MATH]\sum^{m}_{j=1}(3^{m-j}\cdot \prod^{j}_{s=1}2^{a_s} )+3^m \cdot n =2^k[/MATH]. And it should be proven.
2)Yeah I agree. Without context, it seems to be more logical then mathematician problem.
3,4) I try to prove Collatz Conjecture and I have several sheets of paper of cauculations which show equivalence between proving this conjecture and Collatz Conjecture. So it's quite hard to share it all.
 
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