query: Euclidean lemma proof
positive_passages.docid: 75733
positive_passages.text: Divisibility of prime numbers
negative_passages.docid: 60761
negative_passages.text: Proof: $\cos^p (\theta) \le \cos(p\theta)$
negative_passages.docid: 133884
negative_passages.text: A proof using Yoneda lemma
negative_passages.docid: 83665
negative_passages.text: Prove a assertion concerning Lebesgue space
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 18429
negative_passages.text: Counting measure proof
negative_passages.docid: 109325
negative_passages.text: Euclid Lemma proof reasoning
negative_passages.docid: 717
negative_passages.text: Proof of Frullani's theorem
negative_passages.docid: 15851
negative_passages.text: the converse of Schur lemma
negative_passages.docid: 130278
negative_passages.text: Vector Applications in Euclidean Geometry
negative_passages.docid: 146333
negative_passages.text: Gaussian proof for the sum of squares?
negative_passages.docid: 149993
negative_passages.text: Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
negative_passages.docid: 129299
negative_passages.text: Fibonacci sequence and Euclidean algorithm's connection.
negative_passages.docid: 144713
negative_passages.text: Simple Calculus Proof
negative_passages.docid: 40122
negative_passages.text: Why does the Euclidean algorithm work for polynomials? What is the proof?
negative_passages.docid: 91117
negative_passages.text: Schwarz Lemma - like exercise
negative_passages.docid: 133228
negative_passages.text: Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.