Is it possible for both a3
to exist within the interval between n2
a & n are positive integers.
Then a=(n^2+1)^(1/3); and (a+1)^3=((n^2+1)^(1/3)+1)^3,
Which is n^2+(messy factors)+2. Ignore the mess.
But if n^2+2<2n+1, then, rearranging, (n-1)^2<0, which is not possible; so there are no solutions compliant with the requirements of the problem.
Edited on March 11, 2015, 9:07 am
Posted by broll
on 2015-03-11 09:02:39