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On the representation of a number as the sum of a prime and two squares of square-free numbers

Volume 182 / 2018

Christopher Hooley Acta Arithmetica 182 (2018), 201-229 MSC: Primary 11P32. DOI: 10.4064/aa8514-9-2016 Published online: 26 January 2018


Let ${\Upsilon }(n)$ be the number of representations of $n$ as the sum of a prime and the squares of two square-free numbers. Then we find an asymptotic positive lower bound for ${ \Upsilon }(n)$ that implies that all sufficiently large numbers $n$ have such a representation.


  • Christopher HooleySchool of Mathematics
    Cardiff University
    Senghennydd Road
    Cardiff CF24 4AG, United Kingdom

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