query: If $n$ and $p$ are coprime how it will be true for some $x$ and $y$. $Nx+ py = 1$
positive_passages.docid: 63651
positive_passages.text: If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
negative_passages.docid: 71717
negative_passages.text: Is this always true: $P(A|B) = 1-P(A^c|B)$?
negative_passages.docid: 97805
negative_passages.text: $n+1$ is a divisor of $\binom{2n} {n}$
negative_passages.docid: 122115
negative_passages.text: Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
negative_passages.docid: 102042
negative_passages.text: If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
negative_passages.docid: 83752
negative_passages.text: If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
negative_passages.docid: 109778
negative_passages.text: Proving $(x-c)|(p(x)-p(c))$
negative_passages.docid: 127901
negative_passages.text: If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 135768
negative_passages.text: Find $P(n+1)$ for a polynomial P
negative_passages.docid: 128108
negative_passages.text: $Y=\prod_{n\in\mathbb{N}}X$.
negative_passages.docid: 34693
negative_passages.text: Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
negative_passages.docid: 65534
negative_passages.text: Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
negative_passages.docid: 144575
negative_passages.text: Factoring n, where n=pq and p and q are consecutive primes
negative_passages.docid: 81973
negative_passages.text: Definition of $d (P (x ,y )dx)$
negative_passages.docid: 50663
negative_passages.text: prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
negative_passages.docid: 422
negative_passages.text: If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$