Sums of two numbers having only prime factors congruent to one modulo four

Volume 118 / 2019

Rainer Dietmann, Christian Elsholtz Banach Center Publications 118 (2019), 177-179 MSC: Primary 1N25; Secondary 11E25, 11N36, 11P32. DOI: 10.4064/bc118-11


We show that every sufficiently large positive integer congruent to $2$ modulo $4$ can be written as the sum of two positive integers, each having only prime factors congruent to $1$ modulo $4$.


  • Rainer DietmannDepartment of Mathematics
    Royal Holloway
    University of London
    Egham, Surrey, TW20 0EX, United Kingdom
  • Christian ElsholtzInstitute of Analysis and Number Theory
    Graz University of Technology
    Kopernikusgasse 24/II
    A-8010 Graz, Austria

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