UPSC 2015 CDS I Math Paper

Let the two consecutive odd numbers be (2x + 1) and (2x + 3),respectively.
(2x+3)2−(2x+1)2
=4x2+9+12x−4x2−1−4x
=8−8x=8(1−x)‌or‌8K
Thus, we can say that the difference between the squares of two consecutive odd integers is always divisible by 8
Trck:
52−32=25−9=16
which is divisible by 8 and 16.
72−52=49−25=24which is divisible by 8 only.