query: $ab$ divides $a^2+b^2 \implies a=b$
positive_passages.docid: 20593
positive_passages.text: Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
negative_passages.docid: 58654
negative_passages.text: If $|A| > \frac{|G|}{2} $ then $AA = G $
negative_passages.docid: 40626
negative_passages.text: Suppose that $ a,b \in \mathbb{Z}$ If 4 divides $ a^2 + b^2$, then $a$ and $b$ are not odd.
negative_passages.docid: 36602
negative_passages.text: $a^m=b^m$ and $a^n=b^n$ imply $a=b$
negative_passages.docid: 71012
negative_passages.text: If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
negative_passages.docid: 63931
negative_passages.text: When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
negative_passages.docid: 13914
negative_passages.text: If $a^2+b^2=c^2$ then $a$ or $b$ is even.
negative_passages.docid: 138894
negative_passages.text: Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
negative_passages.docid: 130281
negative_passages.text: Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
negative_passages.docid: 45760
negative_passages.text: if G is generated by {a,b} and ab=ba, then prove G is Abelian
negative_passages.docid: 72507
negative_passages.text: Does $ab=1$ imply $ba=1$ in a ring?
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 10236
negative_passages.text: Show that $a^n \mid b^n$ implies $a \mid b$
negative_passages.docid: 118981
negative_passages.text: Proving $\sqrt{ab} = \sqrt a\sqrt b$
negative_passages.docid: 113994
negative_passages.text: Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
negative_passages.docid: 94516
negative_passages.text: If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$