1. $n(n \geqslant=2)$ players participate in a competition that lasts for $k$ days, with each player scoring exactly $1,2, \cdots, n$ points each day (no two players have the same score). At the end of $k$ days, each player's total score is 26. Find all possible values of $(n, k)$.
(22nd Canadian Intermediate Mathematics Competition)
(Cue: Calculate the total score of $n$ players, with $k(1+2+\cdots+n)=26n$, then $k(n+1)=52$. And $52=2^{2} \times 13$, which has 6 factors: $1,2,4,13,26,52$. Also, $n+1 \geqslant 3, k \geqslant 2$. Thus, we get three solutions, namely $(n, k)=(25,2),(12,4),(3,13)$.)