Suppose that a positive integer $n$ is given. Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that
for any polynomial $P$ with positive integer coefficients, with at least $n$ nonzero coefficients; and for any pair of positive integers $a,b$;
if $P(a)$ divides $P(b)$; then $Q(a)$ also divides $Q(b)$, where $Q$ is the polynomial obtained by substituting coefficients $c$ of $P$ by $f(c)$.
Diophantine-ness Preserving Functional equation(Self-made)
- Fm Jakaria
- Posts:79
- Joined:Thu Feb 28, 2013 11:49 pm
You cannot say if I fail to recite-
the umpteenth digit of PI,
Whether I'll live - or
whether I may, drown in tub and die.
the umpteenth digit of PI,
Whether I'll live - or
whether I may, drown in tub and die.