Question 72
Find the least positive integer $N \gt 1$ satisfying the following two properties:
- There exists a positive integer $a$ such that $N = a(2a - 1)$.
- The sum $1 + 2 + \cdots + (N - 1)$ is divisible by $k$ for every integer $1 \leq k \leq 10$.
- There exists a positive integer $a$ such that $N = a(2a - 1)$.
- The sum $1 + 2 + \cdots + (N - 1)$ is divisible by $k$ for every integer $1 \leq k \leq 10$.