1135.lean`

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1 declarations, 1 contain sorry, 0 declared as axioms

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.

Imports (2)

theorem Erdos1135.erdos_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 sorry line 47 source
Source documentation
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.

depends on sorry what this means
Statement uses: Nat, GT.gt, OfNat.ofNat, Exists, Eq, Nat.iterate, CollatzConjecture.collatzStep
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1135 : type_of% CollatzConjecture.collatz_conjecture := by sorry
…
```
Mentions: CollatzConjecture.collatz_conjecture