MathDB

For integers

a

and

b

with

0 \leq a,b < {2010}^{18}

let

S

be the set of all polynomials in the form of

P(x)=ax^2+bx.

For a polynomial

P

S,

if for all integers n with

0 \leq n <{2010}^{18}

there exists a polynomial

Q

S

satisfying

Q(P(n)) \equiv n \pmod {2010^{18}},

then we call

P

as a good polynomial. Find the number of good polynomials.

Problem Statement