query: Show that $(a,b)= ((p,q)*(c,d))+(r,s) $
positive_passages.docid: 23721
positive_passages.text: Prove that the Gaussian Integer's ring is a Euclidean domain
negative_passages.docid: 18119
negative_passages.text: Show that if a,b,c,d are positive then $\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$
negative_passages.docid: 43478
negative_passages.text: Prove that: $ m_a + m_b + m_c \le 4R + r $
negative_passages.docid: 76188
negative_passages.text: Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
negative_passages.docid: 19457
negative_passages.text: Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
negative_passages.docid: 29935
negative_passages.text: If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
negative_passages.docid: 115583
negative_passages.text: prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
negative_passages.docid: 14480
negative_passages.text: Proving $(P(AB))^2+(P(AB^c))^2+(P(A^cB))^2+(P(A^cB^c))^2\ge\frac{1}{4}$ for any events $A$ and $B$
negative_passages.docid: 62755
negative_passages.text: The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
negative_passages.docid: 1962
negative_passages.text: Polynomial $P(a)=b,P(b)=c,P(c)=a$
negative_passages.docid: 5149
negative_passages.text: Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
negative_passages.docid: 6777
negative_passages.text: Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
negative_passages.docid: 91285
negative_passages.text: Prove $a+b+c+d $ is composite
negative_passages.docid: 43219
negative_passages.text: If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
negative_passages.docid: 46106
negative_passages.text: Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
negative_passages.docid: 21726
negative_passages.text: Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
negative_passages.docid: 63879
negative_passages.text: Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$