query: Show that if $(x,y) =1$ then $(x-y, x+y)$ is either $1$ or $2$.
positive_passages.docid: 15168
positive_passages.text: If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
negative_passages.docid: 108873
negative_passages.text: How would one be able to prove mathematically that $1+1 = 2$?
negative_passages.docid: 31937
negative_passages.text: How do I prove equality of x and y?
negative_passages.docid: 100361
negative_passages.text: Show that ord$_{p}2 = 2^{n + 1}$.
negative_passages.docid: 125274
negative_passages.text: For $x+y=1$, show that $x^4+y^4\ge \frac{1}{8}$
negative_passages.docid: 152311
negative_passages.text: Proving expression$\geq 2$, where variables are $x,y,z$
negative_passages.docid: 109778
negative_passages.text: Proving $(x-c)|(p(x)-p(c))$
negative_passages.docid: 13572
negative_passages.text: $x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 68990
negative_passages.text: Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$
negative_passages.docid: 94218
negative_passages.text: Showing $d(x,y) = \frac{|x-y|}{1+|x-y|}$ is a distance.
negative_passages.docid: 136427
negative_passages.text: Given $∃y.∀x.p(x,y)$, use the Fitch system to prove $∀x.∃y.p(x,y)$
negative_passages.docid: 155757
negative_passages.text: Number theory: $x^y + 1 = y^x$
negative_passages.docid: 39908
negative_passages.text: Finding the error in this proof that 1=2
negative_passages.docid: 73716
negative_passages.text: Let $x,y,z>0$ and $x+y+z=1$, then find the least value of ${{x}\over {2-x}}+{{y}\over {2-y}}+{{z}\over {2-z}}$
negative_passages.docid: 86285
negative_passages.text: Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square