UPSC 2013 CDS 2 Math Paper

Remember:
Any number k when divided by 4will be in the form of 4k,4k+1,4k+2 and 4k+3
Here squares of 1, 2 and 3 are 1, 4 and 9, respectively, which is in the form of 4k or 4k+1
For example
4=4×1, which is of the form 4k
16=4×4, which is of the form 4k
9=4×2+1, which is of the form 4k+1
25=4×6+1, which is of the form4k + 1
Therefore, every square integer is of the form 4k or 4k+1.