engleski

Products of factorials which are powers,

Extending earlier research of Erdos and Graham, we consider the problem of products of factorials yielding perfect powers. On the one hand, we describe how the representability of ℓ-th powers behaves when the number of factorials is smaller than, equal to or larger than ℓ, respectively. On the other hand, we investigate the problem that, for which fixed n = b1 it is possible to find integers b2, . . . , bk at most b1 (obeying certain conditions) such that b1!b2! · · · bk! is a perfect power. Here we distinguish the cases where the factorials may be repeated or are distinct.

Products of factorials, perfect powers

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