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We partially answer the question of which bivariate linear equations have infinitely many solutions in $\\text{PS}(\\alpha)$: if $a, b \\in \\mathbb{R}$ are such that the equation $y=ax+b$ has infinitely many solutions in the positive integers, then for Lebesgue-a.e. $\\alpha > 1$, it has infinitely many or at most finitely many solutions in $\\text{PS}(\\alpha)$ according as $\\alpha < 2$ "},"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":"1511.04274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-13T13:24:34Z","cross_cats_sorted":[],"title_canon_sha256":"37de71e108418874a92d02f2a3096c5f146e35098bbf50cb89cd5eee6889fe21","abstract_canon_sha256":"b98b19c71ce4f553d3a0b2440ca70e22e236841695b0f9cb5d39a67874f2a27d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:50.183147Z","signature_b64":"j1gWZt6mMkKhWCCnwOIzymnKanfmblQPkqF19Kzq3XInNDCEqFBYKj9/wWeQ9lWU4NdSbSxZqC3zlnehE+/KCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da86da827529ae0ce51fa9e227af4a6add4254e2b2d58ccf9ffd9cf0c51dd3b0","last_reissued_at":"2026-05-18T01:11:50.182808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:50.182808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions to certain linear equations in Piatetski-Shapiro sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Glasscock","submitted_at":"2015-11-13T13:24:34Z","abstract_excerpt":"Denote by $\\text{PS}(\\alpha)$ the image of the Piatetski-Shapiro sequence $n \\mapsto \\lfloor n^{\\alpha} \\rfloor$ where $\\alpha > 1$ is non-integral and $\\lfloor x \\rfloor$ is the integer part of $x \\in \\mathbb{R}$. 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