Hi, I'm not sure how to solve this question for quadratic probing. My issue is that there are infinite numbers of prime numbers greater than 3, how would we prove them all. Any hints would be helpful

Suppose that we have an open addressing hash table whose size m is a prime number greater than 3, and that we are using quadratic probing of the following form h(k, i) = (h(k) + i2) mod m, = 0,1,2 Prove that, if the hash table contains less than [m/2] keys (i.e, the table is less than haffl), then the insertion of a new key is guaranteed to be successful, i.c., the probing mst be able to reach a free slot. Hint: What if the first |m/2] probe locations for a given key are all distinct? Try proof by contradiction