my question
Find the numbers of the form $\overline{abcd}$ for which the relations are checked simultaneously:
i) $\overline{ab}$ and $\overline{cd}$ are consecutive natural numbers
ii) $(2*\overline{ab}+3)(2*\overline{ab}+7)=\overline{abcd}$.
my idea and the point I got stuck at
The point I got stuck at is if $\overline{ab}=\overline{cd}+1$. Hope one of you can help me!!!
To solve $4x^2-81x+22=0$, you could either use the quadratic formula, or since you only care about integer solutions, you can just try divisors of $22$. Neither $1,2,11,$ nor $22$ work, so it has no positive integer solutions.