Question 49
On the board is written a (not necessarily positive) integer. In a move, if the current number on the board is $a$, one erases it and replaces it by either $a^2 + 2a + 3$ or $5a^2 + 2$ or $a - 119$. Is there a starting number $s$ such that for any positive integer $f$ one can reach $f$ from $s$ with finitely many moves?