On the sum of the square of a prime and a square-free number

Adrian W. Dudek, David J. Platt

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We prove that every integer n ≥ 10 such that n ≢ 1 mod 4 can be written as the sum of the square of a prime and a square-free number. This makes explicit a theorem of Erdos 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's numerical computation regarding the generalised Riemann hypothesis to extend the explicit bounds of Ramaré-Rumely.

    Original languageEnglish
    Pages (from-to)16-24
    Number of pages9
    JournalLMS Journal of Computation and Mathematics
    Volume19
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2016

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