Is there $a,b,c,d\in \mathbb N$ so that $a^2+b^2=c^2$, $b^2+c^2=d^2$?
45356
Are there any positive integers $a, b, c, d$ such that both $(a, b, c)$ and $(b, c, d)$ are Pythagorean triples?
33633
Re:$ (a,b,c,d)=(pr+qs, qr-ps,pr-qs,ps+qr) $
4333
Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
26861
$a+b=c \times d$ and $a\times b = c + d$
114393
If $a$ is divisible by $4$, then there exist int $b$ and $c$ such that $a = b^2 - c^2$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
69874
Are there any integer solutions to $a^3=b^2$?
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
113168
If $a > b$, is $a^2 > b^2$?
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$