Number theory problem related to Collatz conjecture (but NOT the demonstration of the conjecture)

Job ID: 38644721

Budget: €30 – €250 EUR

This project consists in proving a lemma related to Collatz's conjecture.
The idea to prove is that each operation reduces the quantity of "1"s when using a binary notation of this number. The method of demonstration is free, but the preferred method is reasoning by induction (as already started in the document).
Your bid will be accepted only if you are a real mathematician, not just an university student.
Related categories: Statistics Research Writing Mathematics