Quadratic Equation Based Problem:Prove either $a = 2l$ & $b = m$ or $b + m = al$
29540
Method to eliminate $x$ between the equation $x^2 + ax + b = 0$ and $xy+ l(x + y) + m = 0$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
13026
Prove that if AB=I_m, then rk(A)=rk(B).
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
60006
Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
80982
Solve $a^3+b^3+3ab=1$ with $(a,b)\in \Bbb{Z}^2$
110297
Problem related to quadratic equations
145447
bilinear form - proof
117352
Show $x^n+ax+b=0$ has most two solutions
6621
Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$
30835
Logarithm proof problem: $a^{\log_b c} = c^{\log_b a}$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
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 $
103499
$x^2 \equiv a \mod p$, $\ x^2 \equiv b \mod p$, and $x^2 \equiv ab \mod p$, prove either all three are solvable or exactly one
29462
Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$