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
(x4 + 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
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Posted by Jer
on 2020-11-17 10:35:13 |
Solution
