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Erdős problem 1108

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For each k≥2k \geq 2, does the set A={∑n∈Sn!:S⊂N finite}A = \left\{ \sum_{n\in S}n! : S\subset \mathbb{N}\text{ finite}\right\} of all finite sums of distinct factorials contain only finitely many kk-th powers?

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Problem row
sha256:dae27589074872cd1263cde90f12574a4c86eb5f13fefd95ace1f915fed50560
Metadata
sha256:9f76bef22f70bd74d6ad65d19aa8389803aed9227d5716092caa44c89c0ba095
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:b4fccd7bd5a467cadfa752290c1b6f2580b1405a532a73ac500073799fe0e76d
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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