Let $p|ab$-prime. We will compare $v_p(ab)$ and $v_p((cd)^{max(a,b)})$ $v_p(a) \leq a$ - easy to show If $p|a,p|b \to p|c,p|d$ and from $v_p(a) \leq a$ follows that $v_p(ab) \leq a+b \leq 2max(a,b) \leq max(a,b) (v_p(cd))=v_p((cd)^{max(a,b)}) $ If $p|a, p \not |b$ then $v_p(ab)=v_p(a) \leq max(a,b) \leq v_p(c^{max(a,b)}) \leq v_p((cd)^{max(a,b)})$

This is not the 2016 Indonesia MO.

MAKEANALITGREATAGAIN2018 wrote: This is not the 2016 Indonesia MO. Then what is the correct problem for the 2016 INAMO?

Here's the correct problem from the 2016 Indonesian MO for Problem 5: Given a real number $x$. Define the sequence $\{a_n\}_{n=1}^{\infty}$ as $a_n = \lfloor nx \rfloor$ for all natural numbers $n$. If the sequence $\{a_n\}_{n=1}^{\infty}$ is an arithmetic sequence, must $x$ be an integer?