Clearly the expression in the middle equals zero if n is a 4th power and will increase until n is the next power of 4. So were looking for n to be 1 more than a power of 4: n=x^4+1 for whole number x.
This substitution gives us
(x^{4} + 1)^{1/4 } 1
A quick table shows the first value of x to be 30, which yields 9.26*10^6
So the solution is n=30^4+1=810001
(It may be possible to avoid a table with some calculus.)
Edited on November 17, 2020, 10:48 am

Posted by Jer
on 20201117 10:35:13 