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  • 1 Eötvös Loránd University Department of Algebra and Number Theory Pázmány Péter sétány 1/c H-1117 Budapest Hungary Pázmány Péter sétány 1/c H-1117 Budapest Hungary
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Abstract  

Let a1<a2<... be an infinite sequence of positive integers, let k≥2 be a fixed integer and denote by Rk(n) the number of solutions of n=ai1+ai2+...+aik. P. Erdős and A. Srkzy proved that if F(n) is a monotonic increasing arithmetic function with F(n)→+∞ and F(n)=o(n(log n)-2) then |R2(n)-F(n)| =o((F(n))1/2) cannot hold. The aim of this paper is to extend this result to k>2.

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