Let k be an arbitrary given positive integer and let f(x) ∈ Z[x] be a quadratic polynomial with D as its discriminant and a as the coefficient of its quadratic term.Associated to the least common multiple lcm0≤i≤k{f(n + i)} of any k + 1 consecutive terms in the quadratic progression {f(n)}n∈N*, we define the function gkj(n) :=(Πk=0 |f(n +i)|)/lcm0≤i≤k{f(n + i)} for all positive integers n ∈ N* Zk,f, where Zkj :=Uki=0{n ∈N* : f(n + i) =0}.Let Kf :={j ∈ N* : D ≠ a2i2 for all integers i with 1 ≤ i ≤ j}.