458.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 458

Reference: erdosproblems.com/458

Imports (1)

FormalConjecturesUtil

def Erdos458.lcm_upto The least common multiple of the integers in the set $\{1, \dots, n\}$ line 32 source
Source documentation
The least common multiple of the integers in the set $\{1, \dots, n\}$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset.lcm, Finset.Icc, OfNat.ofNat, id
6 instances, coercions and auxiliary constants left out.
```
def lcm_upto (n : ℕ) : ℕ :=
…
```
theorem Erdos458.erdos_458 Let $\operatorname{lcm}(1, \dots, n)$ denote the least common multiple of $\{1, \dots, n\}$ sorry line 41 source
Source documentation
Let $\operatorname{lcm}(1, \dots, n)$ denote the least common multiple of $\{1, \dots, n\}$. Let $p_k$ be the $k$-th prime. Is it true that for all $k \geq 1$, $\operatorname{lcm}(1, \dots, p_{k+1}-1) < p_k \cdot \operatorname{lcm}(1, \dots, p_k)$?

depends on sorry what this means
Statement uses: Iff, True, Nat, LT.lt, Erdos458.lcm_upto, HSub.hSub, Nat.nth, Prime, HAdd.hAdd, OfNat.ofNat, HMul.hMul
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
18 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_458 :
    answer(sorry) ↔ ∀ k : ℕ, lcm_upto ((k + 1).nth Prime - 1)
     < k.nth Prime * lcm_upto (k.nth Prime) := by
…
```
Mentions: Erdos458.lcm_upto