Show that for each natural number $n$, there exist $n$ distinct natural numbers whose sum is a square and whose product is a cube.
Problem
Source: Indian Postal Coaching 2008 set 5 p4
Tags: number theory, Perfect Square, perfect cube
Source: Indian Postal Coaching 2008 set 5 p4
Tags: number theory, Perfect Square, perfect cube
Show that for each natural number $n$, there exist $n$ distinct natural numbers whose sum is a square and whose product is a cube.