Find all pairs of positive integers $a,b$ such that $\frac{a^3+b^3}{ab+4}=2020$
94105
Find the all positive integer solutions $(a,b)$ to $\frac{a^3+b^3}{ab+4}=2020$.
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
95103
A rational matrix such that $A^{2017}=I_n$
72670
Find three distinct triples (a, b, c) consisting of rational numbers that satisfy $a^2+b^2+c^2 =1$ and $a+b+c= \pm 1$.
137626
If $a,b,c$ are positive integers,and $\cfrac{a}{b}+\cfrac{b}{c}+\cfrac{c}{a}$ and $\cfrac{b}{a}+\cfrac{c}{b}+\cfrac{a}{c}$ are integers then $a=b=c$
23638
$a^2b^2+a^2c^2+b^2c^2\leq 3$
69874
Are there any integer solutions to $a^3=b^2$?
101708
Integers can be expressed as $a^3+b^3+c^3-3abc$
153053
Find numbers $a, b, c$ given that $a+b+c=12$, $a^2+b^2+c^2=50$, and $a^3+b^3+c^3=168$
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
77547
Find integers $a,b,c,d$ such that
11868
Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$
96861
How find all ordered pairs $(m,n)$ such $\frac{n^3-1}{mn-1}$ is an integer
83910
Integer part of $\sqrt[3]{24+\sqrt[3]{24+\sqrt[3]{24+\cdots}}}$
69328
(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
148671
Trying to factor $x^4-3$ over $\Bbb{F}_p$ with $p\equiv 3\mod{4}$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.