PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 63 (77), pp. 21--25 (1998)
Atkin's theorem on pseudo-squares
R. Balasubramanian and D.S. RamanaInstitute for Mathematical Sciences, Chennai, India
Abstract: We give an elementary proof of a theorem of A.O.L. Atkin on psuedo-squares. As pointed out by Atkin, from this theorem it immediately follows that there exists an infinite sequence of positive integers, whose $j$ th term $s(j)$ satisfies $s(j)=j^2 + O(\log(j))$, such that the set of integers representable as a sum of two distinct terms of this sequence is of positive asymptotic density.
Classification (MSC2000): 11B13
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