[{"doi":"10.1016/j.jnt.2022.04.006","keyword":["Pseudo-polynomials","Chinese remainder theorem","Ruzsa’s conjecture"],"OA_place":"repository","abstract":[{"text":"We explore two questions about pseudo-polynomials, which\r\nare functions f : N → Z such that k divides f(n + k) −\r\nf(n) for all n, k. First, for certain arbitrarily sparse sets R, we\r\nconstruct pseudo-polynomials f with p|f(n) for some n only if\r\np ∈ R. This implies that not all pseudo-polynomials satisfy an\r\nassumption of a recent paper of Kowalski and Soundararajan.\r\nWe also consider α-primary pseudo-polynomials, where the\r\npseudo-polynomial condition is only required for k lying in\r\na set of primes of density α. We show that if an α-primary\r\npseudo-polynomial is O(e(β−)n), where β = √7\r\n3 − 1\r\n6 ≈ 0.715,\r\nthen it is a polynomial.","lang":"eng"}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"22196","author":[{"first_name":"Vivian Zieve","full_name":"Kuperberg, Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697","last_name":"Kuperberg"}],"date_updated":"2026-07-14T11:08:14Z","arxiv":1,"fulldoi":"https://doi.org/10.1016/j.jnt.2022.04.006","publisher":"Elsevier","oa_version":"Preprint","day":"18","volume":241,"external_id":{"arxiv":["2006.02527"]},"oa":1,"page":"531-541","month":"05","title":"On pseudo-polynomials divisible only by a sparse set of primes and α-primary pseudo-polynomials","date_published":"2022-05-18T00:00:00Z","article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2006.02527","open_access":"1"}],"year":"2022","article_type":"original","publication_status":"published","publication_identifier":{"issn":["0022-314X"]},"date_created":"2026-06-29T12:58:07Z","OA_type":"green","extern":"1","intvolume":"       241","scopus_import":"1","quality_controlled":"1","publication":"Journal of Number Theory","type":"journal_article","citation":{"chicago":"Kuperberg, Vivian Zieve. “On Pseudo-Polynomials Divisible Only by a Sparse Set of Primes and α-Primary Pseudo-Polynomials.” <i>Journal of Number Theory</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jnt.2022.04.006\">https://doi.org/10.1016/j.jnt.2022.04.006</a>.","short":"V.Z. Kuperberg, Journal of Number Theory 241 (2022) 531–541.","ama":"Kuperberg VZ. On pseudo-polynomials divisible only by a sparse set of primes and α-primary pseudo-polynomials. <i>Journal of Number Theory</i>. 2022;241:531-541. doi:<a href=\"https://doi.org/10.1016/j.jnt.2022.04.006\">10.1016/j.jnt.2022.04.006</a>","apa":"Kuperberg, V. Z. (2022). On pseudo-polynomials divisible only by a sparse set of primes and α-primary pseudo-polynomials. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2022.04.006\">https://doi.org/10.1016/j.jnt.2022.04.006</a>","mla":"Kuperberg, Vivian Zieve. “On Pseudo-Polynomials Divisible Only by a Sparse Set of Primes and α-Primary Pseudo-Polynomials.” <i>Journal of Number Theory</i>, vol. 241, Elsevier, 2022, pp. 531–41, doi:<a href=\"https://doi.org/10.1016/j.jnt.2022.04.006\">10.1016/j.jnt.2022.04.006</a>.","ista":"Kuperberg VZ. 2022. On pseudo-polynomials divisible only by a sparse set of primes and α-primary pseudo-polynomials. Journal of Number Theory. 241, 531–541.","ieee":"V. Z. Kuperberg, “On pseudo-polynomials divisible only by a sparse set of primes and α-primary pseudo-polynomials,” <i>Journal of Number Theory</i>, vol. 241. Elsevier, pp. 531–541, 2022."},"status":"public"}]