Geodesic
On the representation of a~number as a~sum of the $k$-th powers in an arithmetic progression
Algebra and discrete mathematics, no. 2 (2003), pp. 87-92.

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In this paper we obtain the asymptotic formula for a natural $n\leq x$ which representate as a sum of two non-negative $k$-th powers in an arithmetic progression.
Keywords: asymptotic formula, exponential sum, number of representation. 
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     title = {On the representation of a~number as a~sum of the $k$-th powers in an arithmetic progression},
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N. S. Prosyanyuk. On the representation of a~number as a~sum of the $k$-th powers in an arithmetic progression. Algebra and discrete mathematics, no. 2 (2003), pp. 87-92. http://geodesic.mathdoc.fr/item/ADM_2003_2_a4/