Question 26
For integers $(a,b)$ set $P(x)=ax^3+bx$. Call $(a,b)$ $m$-sufficient if, for all integers $x,y$, $m\mid P(x)-P(y)$ implies $m\mid x-y$. Call it very sufficient if it is $k$-sufficient for infinitely many positive integers $k$. Does there exist a pair that is 1110-sufficient but not very sufficient?