Prove there does not exist $(a, b, c, d)$, not all $0$, such that $ a^2 + b^2 = 3(c^2+d^2)$
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
153241
Four different positive integers a, b, c, and d are such that $a^2 + b^2 = c^2 + d^2$
136868
Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
62982
Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
139
Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
69874
Are there any integer solutions to $a^3=b^2$?
44309
Prove $5a^2 ≠ 3b^2$ for all non-zero rational numbers $a$ and $b$
147952
Why can we prove mathematically that a formula to solve an (n+5) order polynomial does not exist?
91786
Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
80720
What paths to choose to prove that $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 - y^2}$ does not exist?
145558
Prove that $2^n+3^n $ is never a perfect square
113359
Proving that $x^2 + 4$ is not divisible by $3$
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
18203
Diophantine equation $a^2+b^2=c^2+d^2$