if $x^2+ax+b=0$ has an integer root, show that it divides b
107089
finding rational roots of polynomials
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
29540
Method to eliminate $x$ between the equation $x^2 + ax + b = 0$ and $xy+ l(x + y) + m = 0$
15730
Determine the minimum of $a^2 + b^2$ if $a,b\in\mathbb{R}$ are such that $x^4 + ax^3 + bx^2 + ax + 1 = 0$ has at least one real solution
114872
If $ax^2-bx+c=0$ has two distinct real roots lying in the interval $(0,1)$ $a,b,c$ belongs to natural prove that $\log_5 {abc}\geq2$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
123441
Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
126445
Proving the second root of a quadratic equation
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
92543
Regular expressions: Show that A*B is the solution of X = AX + B
44020
Probability of $x^2+bx+c=0$ having real roots
118467
Prove that $a^2+ab+b^2\ge 0$