Let $n$ be a positive integer and let $$1 = d_1 < d_2 < d_3 < d_4$$the four smallest divisors of $n$. Find all$ n$ such that $$n^2 = d_1 + d_2^2+d_3^3 +d_4^4.$$
Source: 2011 Cuba MO 2.3
Tags: number theory, Divisors
Let $n$ be a positive integer and let $$1 = d_1 < d_2 < d_3 < d_4$$the four smallest divisors of $n$. Find all$ n$ such that $$n^2 = d_1 + d_2^2+d_3^3 +d_4^4.$$