UPSC 2017 CDS I Math Paper

Two consecutive integers can be written in the form 2m and 2m + 1.
Here, 2m is an even integer and (2m + 1) is an odd integer.
So, of the two consecutive integers, one is even.
Hence, statement 1 is correct
Remember: The product of two consecutive integers is always divisible by 2.
(2m+1)2=4m2+4m+1
=4m(m+1)+1
=4×2n+1=8n+1
Thus, the square of an odd integer is of the form 8n+1.
Hence, statement 2 is correct.