1.determine the set of integers 'n' for which
n2+19n+92 is a square
When n is positive then the given expression lies between (n+9)2 and (n+10)2 which are squares of two consecutives. This means no solution. When n is negative take n=-p where p is positive then p2-19p+92 expression lies between (p-9)2 and (p-10)2 for p>11. Keep on putting p=1,2,3 and so on upto 11 for perfect square. I've not checked all but p=8 meaning n=-8 should be a solution.