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For my math internal assessment, I'm looking at the Collatz Conjecture and different ways to try and solve it.
I wanted to see if there were any possible partial solutions for it by which I mean if we take a specific type of number the conjecture would be true for all of those numbers.
For example, the collatz conjecture is true for all m where m=2^n since the powers of two will keep being even until it reaches one. However, I wanted a more complex proof for another type of numbers(Say, for all powers of 3 or for all prime numbers if it were possible) so I wanted to know if there are any such partial proofs you could think of