Prove that $(2m+1)^2 - 4(2n+1)$ can never be a perfect square where m, n are integers I could prove it hit and trial method. But I was thinking to come up with a general and a more 'mathematically' correct method, but I did not reach anywhere. Thanks a lot for any help.

an odd^2 is always of the form 8k+1.now if it is a ssquare then it wiil be of the form 8k+1.again (2m+1)^2 will be of the form some 8t+1 i.e. 4(2n+1) will be divisible by 8 which leads to contradiction
