- Find all (positive or negative) integers $n$ for which
is a perfect square. Remember that you must justify that you have found them all.
For the first part I did so:
$$n^2+20n+11=M^2 $$ where M is an integer. That factors down to: $$ (n+10)^2-M^2=89$$ $$ (n+10-M)(n+10+M)=89$$ From there it is easy to find solutions as 89 is prime and it is a diophantine equation.
So the first part of the question is quite simple, however I am completely stumped on how to do the second part, how might we show that those are the only solutions?