Atkin's Theorem on Pseudo-squares

Balasubramanian, R. ; Ramana, D. S. (1998) Atkin's Theorem on Pseudo-squares Publications de l'Institut Mathématique, 63 (77). pp. 21-25. ISSN 0350-1302

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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.

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