Solve the equation $$2xy + 3y^{2} = 24, \qquad x, y \in \mathbb{Z}$$
I tried by stating that $x$ and $y$ cannot both be odd and that y cannot be odd. So either $x$ and $y$ are both even or $x$ is even and $y$ is odd. Then I was trying take the residues modulo $3$ and modulo $8$ but could not arrive at a conclusion. Please help me solve this further.
Best Answer
Equation can be written as $y*(2x+3y)=24$. Thus $y$ must be an integer factor of $24$. This should get you to a manageable range of possibilities.