Question

Find all integers n(positive, negative or zero) for which n^2 + n + 41 is a perfect square.

Answer 1

write it up as
n^2 + n + 41 = m^2
n + 41 = (m-n)(m+n)
note that m-n>0 and m-n < 7
put m-n = 1,2, ...,6 and try to solve for for integer value of n.

if you get integer value of n, then that's your answer for n.

finally you should get this result
http://www.wolframalpha.com/input/?i=n%5E2+%2B+n+%2B+41++%3D+m%5E2+Interger+solution

Answer 2

Thank you sir