How can I prove that $a^2 + b^2 = c^2$ in a hyperbola?
44349
A geometric reason why the square of the focal length of a hyperbola is equal to the sum of the squares of the axes?
18606
How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
18203
Diophantine equation $a^2+b^2=c^2+d^2$
130952
Finding the conjugate hyperbola
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
31104
$a+b+c =0$; $a^2+b^2+c^2=1$. Prove that: $a^2 b^2 c^2 \le \frac{1}{54}$
97750
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
60355
Find a formula for all the points on the hyperbola $x^2 - y^2 = 1$? whose coordinates are rational numbers.
34275
How do I show that $\frac {a^2}b + \frac {b^2}c + \frac {c^2}d + \frac {d^2}a \ge 4$ for $a^2 + b^2 + c^2 + d^2 = 4$?
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
65297
Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$.