On the Least Common Multiple of Polynomial Sequences at Prime Arguments
Abstract
Cilleruelo conjectured that if f∈Z[x] is an irreducible polynomial of degree d 2 then, lcm \f(n) n<x\ (d-1)x x. In this article, we investigate the analogue of prime arguments, namely, lcm \f(p) p<x\ where p denotes a prime and obtain non-trivial lower bounds on it. Further, we also show some results regarding the greatest prime divisor of f(p).
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