On the least common multiple of polynomial sequences at prime arguments.

Cilleruelo conjectured that if f ∈ ℤ [ x ] is an irreducible polynomial of degree d ≥ 2 then, log lcm { f (n) | n < x } ∼ (d − 1) x log x. In this paper, we investigate the analog of prime arguments, namely, lcm { f (p) | p < x } , where p denotes a prime and obtain nontrivial lower bounds on it. Further, we also show some results regarding the greatest prime divisor of f (p). [ABSTRACT FROM AUTHOR]