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We define the $S$-part $[m]_S$ of $m$ by $[m]_S := q_1^{r_1} \\ldots q_s^{r_s}$. Let $(u_n)_{n \\ge 0}$ be a linear recurrence sequence of integers. Under certain necessary conditions, we establish that for every $\\varepsilon > 0$, there exists an integer $n_0$ such that $[u_n]_S\\leq |u_n|^{\\varepsilon}$ holds for $n > n_0$. Our pro"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.00485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-02T07:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"81533a03076d2b15013659078b15521dd5d5f64bb804c2cdda40970721605d8c","abstract_canon_sha256":"3f257f33344173265ac73456940ca7fab60e516d47bfaa752089eb5e24673239"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:32.693185Z","signature_b64":"PMkwP+gtsd+Iue3WstGLfB1cZuqd6ZmqVScIqypDyYgZ62/I9OtOvGbUD8RR82R6NdlyVeVKc5FvWC4xKp5+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c0b405c2823a66b549f5a1cf3c58dbf758624b041883df8ec6a141da6b77f94","last_reissued_at":"2026-05-18T01:00:32.692530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:32.692530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$S$-parts of terms of integer linear recurrence sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jan-Hendrik Evertse, Yann Bugeaud","submitted_at":"2016-11-02T07:14:17Z","abstract_excerpt":"Let $S = \\{q_1, \\ldots , q_s\\}$ be a finite, non-empty set of distinct prime numbers. For a non-zero integer $m$, write $m = q_1^{r_1} \\ldots q_s^{r_s} M$, where $r_1, \\ldots , r_s$ are non-negative integers and $M$ is an integer relatively prime to $q_1 \\ldots q_s$. We define the $S$-part $[m]_S$ of $m$ by $[m]_S := q_1^{r_1} \\ldots q_s^{r_s}$. Let $(u_n)_{n \\ge 0}$ be a linear recurrence sequence of integers. Under certain necessary conditions, we establish that for every $\\varepsilon > 0$, there exists an integer $n_0$ such that $[u_n]_S\\leq |u_n|^{\\varepsilon}$ holds for $n > n_0$. 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