A network routing protocol generates a priority index SSS for a data stream of size k∈Nk \in \mathbb{N}k∈N based on the formula
S=k2+12k+13 S = k^2 + 12k + 13 S=k2+12k+13Use the method of proof by contradiction to show that if the priority index SSS is even, then the data stream size kkk must be odd.