proof of a^2 + ab + b^2 >0; a,b, both are not zero, both are real
118467
Prove that $a^2+ab+b^2\ge 0$
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
14480
Proving $(P(AB))^2+(P(AB^c))^2+(P(A^cB))^2+(P(A^cB^c))^2\ge\frac{1}{4}$ for any events $A$ and $B$
5410
Prove that $a^2 + b^2 \geq 8$ if $ x^4 + ax^3 + 2x^2 + bx + 1 = 0 $ has at least one real root.
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
20110
How to prove $(AB)^T=B^T A^T$
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
44309
Prove $5a^2 ≠ 3b^2$ for all non-zero rational numbers $a$ and $b$
131844
When does $(e^a)^b = e^{ab}$ hold?
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
106011
Proving it has all real roots
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.