How to make polynomial hashing more stable?

Question

Algorithms

Solutions with polynomial hashes are hacked on codeforces .
And how to write, so as not to be hacked?

Answer 1

As they write here

Hashes must be with a randomized multiplier/modulus, and the modulus must be simple, otherwise you will get caught sooner or later!

Answer 2

First, the module P must be simple.
Explanation: H mod P = a, if P is prime, then we get the total number of residues - the number of different values ​​of A will be equal to P (0...P-1). If P is composite, then there will be collisions. This follows from Euler's theorem.
The article says how hashes with P = 2^64 are cracked, which is obviously not prime :)
Secondly, the more P, the better, because. more hash values. Usually they take (10^9)+7
In programming Olympiads, this is enough.
Thirdly (not for Olympiads), it is possible to duplicate hash calculations for several modules P1, P2, P3.
The probability that all three hashes will give a collision is almost unbelievable, but possible.