D both are suffecient.
1) Sum of two consecutive integers always give 1 as remainder.
2) (2m)^2 + (2n+1)^2 when M & N are even and odd
= 4(m^2 + n^2 + n) + 1
D is correct. A small addition for (1) sum of SQUARES of two consequtive integers always gives 1 in a remainder when the sum is divided by 4. Lets prove it quickly.
If M and N are consequtive, then one is even and the other is odd
Let M=2k, and N=2k+1