{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,2]],"date-time":"2022-06-02T19:40:12Z","timestamp":1654198812353},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>We prove that every integer<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157015000297_inline1\" \/><jats:tex-math>$n\\geqslant 10$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>such that<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157015000297_inline2\" \/><jats:tex-math>$n\\not \\equiv 1\\text{ mod }4$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>can be written as the sum of the square of a prime and a square-free number. This makes explicit a theorem of Erd\u0151s that every sufficiently large integer of this type may be written in such a way. Our proof requires us to construct new explicit results for primes in arithmetic progressions. As such, we use the second author\u2019s numerical computation regarding the generalised Riemann hypothesis to extend the explicit bounds of Ramar\u00e9\u2013Rumely.<\/jats:p>","DOI":"10.1112\/s1461157015000297","type":"journal-article","created":{"date-parts":[[2016,1,29]],"date-time":"2016-01-29T10:08:33Z","timestamp":1454062113000},"page":"16-24","source":"Crossref","is-referenced-by-count":0,"title":["On the sum of the square of a prime and a square-free number"],"prefix":"10.1112","volume":"19","author":[{"given":"Adrian W.","family":"Dudek","sequence":"first","affiliation":[]},{"given":"David J.","family":"Platt","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2016,1,1]]},"reference":[{"key":"S1461157015000297_r10","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00669-2"},{"key":"S1461157015000297_r12","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1993-1195435-0"},{"key":"S1461157015000297_r1","unstructured":"1. ACRC, University of Bristol, BlueCrystal Phase 3 User Guide, 2014,https:\/\/www.acrc.bris.ac.uk\/pdf\/bc-user-guide.pdf."},{"key":"S1461157015000297_r9","doi-asserted-by":"crossref","unstructured":"9. D.\u00a0J. Platt , \u2018Numerical computations concerning the GRH\u2019, Math. Comp. (2015), to appear.","DOI":"10.1090\/mcom\/3077"},{"key":"S1461157015000297_r2","unstructured":"2. C. Batut , K. Belabas , D. Bernardi , H. Cohen and M. Olivier , User\u2019s Guide to PARI-GP, 2000,http:\/\/pari.math.u-bordeaux.fr\/pub\/pari\/manuals\/2.3.3\/users.pdf."},{"key":"S1461157015000297_r3","doi-asserted-by":"publisher","DOI":"10.1215\/00127094-2856619"},{"key":"S1461157015000297_r13","unstructured":"13. K. Walisch , PrimeSieve, http:\/\/primesieve.org\/."},{"key":"S1461157015000297_r5","doi-asserted-by":"crossref","unstructured":"5. A.\u00a0W. Dudek , \u2018On the sum of a prime and a square-free number\u2019, Ramanujan J. 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