Find all pairs of integers (c,d), both greater than 1, such that the following holds:For any monic polynomial Q of degree d with integer coefficients and for any prime p>c(2c+1), there exists a set S of at most (2c+12c−1)p integers, such that
s∈S⋃{s,Q(s),Q(Q(s)),Q(Q(Q(s))),…}
contains a complete residue system modulo p (i.e., intersects with every residue class modulo p). number theorycombinatoricsgraph theory