Question 100
Show that there exists a positive constant $C$ such that, for all positive reals $a$ and $b$ with $a + b$ being an integer, we have
$$
\{a^3\} + \{b^3\} \le 2 - \frac{C}{(a+b)^6}.
$$
$$
\{a^3\} + \{b^3\} \le 2 - \frac{C}{(a+b)^6}.
$$
MathNet 2023-part-06 — 191 problems (EN–VI) Question 100
Math Olympiad Vault · MathNet 2023-part-06 — 191 problems (EN–VI)