query: Are there any partial proofs for the collatz conjecture?
positive_passages.docid: 151440
positive_passages.text: Are there specific numbers for which the Collatz Conjecture is proven?
negative_passages.docid: 147111
negative_passages.text: Where is the Proof for the Sum-to-Product rule derrived from?
negative_passages.docid: 125164
negative_passages.text: How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
negative_passages.docid: 144571
negative_passages.text: A conjecture including binomial coefficients
negative_passages.docid: 140153
negative_passages.text: Conjectures Involving floor(x)/piecewise continuity with regards to Integration and Differential Equations
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 85540
negative_passages.text: Prove or Disprove the Existence of Solutions...
negative_passages.docid: 8349
negative_passages.text: What is the status of the purported proof of the ABC conjecture?
negative_passages.docid: 97917
negative_passages.text: Step in the Stein's proof of Plancherel Theorem
negative_passages.docid: 115606
negative_passages.text: Proofs involving $ (A\setminus B) \cup (A \cap B)$
negative_passages.docid: 43490
negative_passages.text: Deriving Bloch's Theorem
negative_passages.docid: 19804
negative_passages.text: How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
negative_passages.docid: 74523
negative_passages.text: Proof by Cases involving divisibility
negative_passages.docid: 38090
negative_passages.text: Partial sums of $nx^n$
negative_passages.docid: 83542
negative_passages.text: A natural problem in $\textrm{S}_2^\textrm{P}$?
negative_passages.docid: 113598
negative_passages.text: Collatz optimization
negative_passages.docid: 136439
negative_passages.text: Where can I read the full proof of the Banach-Mazur theorem?