Countably many
Number Theory
Level
5
There are \(N\) rational numbers \(R \) such that
\[ \sqrt[3] {5\times 10^8 + \sqrt{R} } + \sqrt[3]{5\times 10^8- \sqrt{R} } \]
is an integer. What are the last three digits of \(N\)?
Details and assumptions
You may use the fact that \( 0.7937 < \sqrt[3]{0.5} < 0.793701 \)
We choose the real value of the roots (where applicable).
by
Calvin Lin