A lower bound on the least common multiple of polynomial sequences
- For an irreducible polynomial f∈ℤ[x] of degree d≥2, Cilleruelo conjectured that the least common multiple of the values of the polynomial at the first N integers satisfies loglcm(f(1),…,f(N))∼(d−1)NlogN as N→∞. This is only known for degree d=2. We give a lower bound for all degrees d≥2 which is consistent with the conjecture: loglcm(f(1),…,f(N))≫NlogN.
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