Show that $a^2 + b^2 = c^3 $ has infinitely many solutions
34393
Variation of Pythagorean triplets: $x^2+y^2 = z^3$
26081
What will be total number of solutions of $a+b+c = n$?
112390
Solutions of $x^2 \equiv 1 \pmod N$
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
48127
Are there infinitely many $A\in \mathbb{C}^{2 \times 2}$ satisfying $A^3 = A$?
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
5729
If $a^2+b^2+c^2=1$ then prove the following.
23638
$a^2b^2+a^2c^2+b^2c^2\leq 3$
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
63505
Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
111467
find all natural solution that satisfy $x^2+y^2 = 3z^2$
23835
Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
35066
Nature and number of solutions to $xy=x+y$
144863
Finding integer solutions to $y^2=x^3-2$