Question 128
Let $n$ be a positive integer and let $1 = d_{1} \lt d_{2} \lt d_{3} \lt \ldots \lt d_{k} = n$ be its positive divisors, in increasing order. It is known that $k \geq 4$ and that $d_{3}^{2} + d_{4}^{2} = 2n + 1$.
a. Find all possible values of $k$.
b. Find all possible values of $n$.
a. Find all possible values of $k$.
b. Find all possible values of $n$.