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 squarefree number. This makes explicit a theorem of Erdős 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 language  English 

Pages (fromto)  1624 
Number of pages  9 
Journal  LMS Journal of Computation and Mathematics 
Volume  19 
Issue number  1 
Early online date  29 Jan 2016 
DOIs  
Publication status  Published  1 Feb 2016 
Keywords
 11N13
 11P32 (primary)
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Sadaf R Alam (Manager), Steven A Chapman (Manager), Polly E Eccleston (Other), Simon H Atack (Other) & D A G Williams (Manager)
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