44 C. $3^{4}$ and $4^{4}$ both leave a remainder of 1 when divided by 5. Therefore, when $n=4m, 4m+1, 4m+2, 4m+3$, the remainders of $3^{n}+4^{n}$ when divided by 5 are $2, 2, 0, 1$ respectively. $X=\{4m-2 \mid m \in \mathbf{N}\}$. And $Y=\{t \mid t=4k(k-1)+2, k \in \mathbf{N}\}$, so $Y \subset X$.
44 Set $X=\left\{n \left\lvert\, \frac{3^{n}+4^{n}}{5} \in \mathbf{N}\right., n \in \mathbf{N}\right\}$, Set $Y=\left\{t \mid t=(2 k-1)^{2}+1, k \in\right.$ $\mathbf{N}\}$, the relationship between these two sets is
A. $X=Y$
B. $X \subset Y$
C. $Y \subset X$
D. $X \not \subset Y$ and $Y \not \subset X$