Prove that $A^2$+$B^2$ is rational if $A+B$ and $AB$ are rational
66210
Prove that $z^n + 1/{z^n}$ is a rational number
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
44309
Prove $5a^2 ≠ 3b^2$ for all non-zero rational numbers $a$ and $b$
148310
Showing rational numbers are algebraic
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
105641
Prove that $ab\leq\frac{1}{2\varepsilon}a^2+\frac{\varepsilon}{2}b^2$
45619
Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
85449
Show a,b,c congruences when $a^2+b^2=c^2$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
5694
How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?