Question 49
a) Find all positive integers $n$, such that the sum of all integers from $1$ to $n + 1$ can be represented as the sum of $n$ consecutive integers.
b) Find all positive integers $n$, for which there exists an integer $a$, such that the sum of the integers from $a$ to $a + n$ is equal to the sum of the integers from $a + n + 1$ to $a + 2n$.
b) Find all positive integers $n$, for which there exists an integer $a$, such that the sum of the integers from $a$ to $a + n$ is equal to the sum of the integers from $a + n + 1$ to $a + 2n$.