FormalConjectures.ErdosProblems.«1135»

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import FormalConjectures.Wikipedia.CollatzConjecture

Erdős Problem 1135

The Collatz conjecture states that for any positive integer $n$, there exists a natural number $m$ such that the $m$-th term of the sequence is 1.

References:

erdosproblems.com/1135

[Gu04] Guy, Richard K., Unsolved problems in number theory. (2004), xviii+437.

[La10] Lagarias, Jeffrey C., The {$3x+1$} problem: an overview. (2010), 3--29.

[La16] Lagarias, Jeffrey C., Erdős, Klarner, and the {$3x+1$} problem. Amer. Math. Monthly (2016), 753--776.

[La85] Lagarias, Jeffrey C., The {$3x+1$} problem and its generalizations. Amer. Math. Monthly (1985), 3--23.

This file points to the canonical formalization in FormalConjectures.Wikipedia.CollatzConjecture.


namespace Erdos1135

The Collatz conjecture states that for any positive integer $n$, there exists a natural number $m$ such that the $m$-th term of the sequence is 1.

@[category research open, AMS 11 37]
theorem declaration uses 'sorry'erdos_1135 : type_of% CollatzConjecture.collatz_conjecture := by⊢ ∀ n > 0, ∃ m, CollatzConjecture.collatzStep^[m] n = 1 sorryAll goals completed! 🐙


end Erdos1135