406.lean`

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2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 406

Reference: erdosproblems.com/406

Imports (1)

FormalConjecturesUtil

theorem Erdos406.erdos_406 Is it true that there are only finitely many powers of $2$ which have only the digits $0$ and $1$ when written in base $3$? sorry line 35 source
Source documentation
Is it true that there are only finitely many powers of $2$ which have only the digits $0$ and $1$ when written in base $3$?

depends on sorry what this means
Statement uses: Iff, True, Set.Finite, Nat, Set.ofPred, And, Nat.isPowerOfTwo, HasSubset.Subset, List, Nat.digits, OfNat.ofNat, List.cons, List.nil
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_406 : answer(sorry) ↔ { n | n.isPowerOfTwo ∧ Nat.digits 3 n ⊆ [0, 1] }.Finite := by
…
```
theorem Erdos406.erdos_406.variants.one_two If we only allow the digits $1$ and $2$ then $2^{15}$ seems to be the largest such power of $2$ sorry line 43 source
Source documentation
If we only allow the digits $1$ and $2$ then $2^{15}$ seems to be the largest such power of $2$.

depends on sorry what this means
Statement uses: IsGreatest, Nat, Set.ofPred, And, Nat.isPowerOfTwo, HasSubset.Subset, List, Nat.digits, OfNat.ofNat, List.cons, List.nil, HPow.hPow
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
14 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_406.variants.one_two :
    IsGreatest { n | n.isPowerOfTwo ∧ Nat.digits 3 n ⊆ [1, 2] } (2 ^ 15) := by
…
```