query: weakened version of Dirichlet's theorem - proof without Dirichlet's theorem
positive_passages.docid: 36
positive_passages.text: Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
negative_passages.docid: 123458
negative_passages.text: Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
negative_passages.docid: 36485
negative_passages.text: $H_n(X,A) \not \approx \tilde{H}_n(X/A)$
negative_passages.docid: 26658
negative_passages.text: A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
negative_passages.docid: 76347
negative_passages.text: Shorter proof for some equvalences
negative_passages.docid: 31199
negative_passages.text: Divergence $\int_{-\pi}^{\pi} |D_n(x)|dx$ for Dirichlet kernel as $n\to\infty$
negative_passages.docid: 24478
negative_passages.text: What is the name of this theorem, and are there any caveats?
negative_passages.docid: 64075
negative_passages.text: Prove that a set of connectives is inadequate
negative_passages.docid: 122911
negative_passages.text: Characterization of weak convergence in $\ell_\infty$
negative_passages.docid: 18907
negative_passages.text: Is this proof of $\liminf E_k \subset \limsup E_k $ correct?
negative_passages.docid: 7164
negative_passages.text: Proof of Darboux's theorem
negative_passages.docid: 157432
negative_passages.text: How to use the Mean Value Theorem to prove the following statement:
negative_passages.docid: 146846
negative_passages.text: Why is this function continuous, unlike the Dirichlet function?
negative_passages.docid: 116811
negative_passages.text: Proofs with limit superior and limit inferior: $\liminf a_n \leq \limsup a_n$
negative_passages.docid: 4834
negative_passages.text: Proving that unconditional convergence is equivalent to absolute convergence
negative_passages.docid: 26183
negative_passages.text: Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
negative_passages.docid: 95901
negative_passages.text: Inequality similar to the Schwarz-Pick theorem