VTMO 2026 - Grade 8 - Final - SET 9 - Self-study Question 1

The numbers $2$ and $4$ are on a board. Hung repeatedly chooses numbers $a,b$ already on the board and writes a new number of one of the forms $3a+1$, $5b+2$, or $2ab+a+b$. Can $2024$ ever be among the numbers he writes? Explain.