$\dfrac1a+\dfrac1b=\dfrac1c$, $a, b, c \in \mathbb{N}$ with no common factor, find all solutions
67528
"If $1/a + 1/b = 1 /c$ where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer"
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
124073
solving for one solution to a system of polynomials
69328
(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
77547
Find integers $a,b,c,d$ such that
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
45616
Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers
20957
If $a+\frac1b=b+\frac1c=c+\frac1a$ for distinct $a$, $b$, $c$, how to find the value of $abc$?
68881
Solve for $\theta$: $a = b\tan\theta - \frac{c}{\cos\theta}$
94965
Solve $x\equiv 1\pmod2$, $x\equiv 2\pmod3$, $x\equiv 3\pmod4$, $x\equiv 4\pmod5$, $x\equiv 5\pmod6$ and $x\equiv 0\pmod7$
137015
Solutions for $a^2+b^2+c^2=d^2$
114011
Algebra - Solving for three unknowns.
89705
How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?
33314
How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?
105302
Solutions of bivariate cubic Diophantine equation
19896
Prove $\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\geq \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}$