Normally when we do string hashing, we use values 1...26. Can we do such a hash for values 1...N where N is 50000? I think it is maybe more error, but is there some bound on N for which we can safely use polynomial hash?
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From what I have read about hashing, I think the hash should be working fine for large N(=50000) as well.
A good link for this is : Zlobober's comment in Anti-Hash test discussion, where he mentions about distribution of hash value to be nearly a uniform-distribution over the field. I remember once using it for large values, and still getting Accepted. The key is using multiple hashes.