Prove $x^2=y^3$ where $x,y\in \mathbb{Z}$ implies $x=a^3$ and $y=b^2$ where $a,b\in\mathbb{Z}$
69874
Are there any integer solutions to $a^3=b^2$?
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
153532
Proving $a^2$ is even $\implies$ $a$ is even by contradiction
77763
Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
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
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
20626
Prove that $x^y < y^x$
99739
The diophantine equation $x^2+y^2=3z^2$
87029
Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$
44309
Prove $5a^2 ≠ 3b^2$ for all non-zero rational numbers $a$ and $b$
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
20964
Proof that $n^2 < 2^n$