Abstract
In this note we generalize Linnik's result on the representation of numbers as the sum of two squares and three cubes to the case of a binary quadratic and a ternary cubic form under certain restrictions.
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Yu. (J.) V. Linnik, “Additive problems involving squares, cubes and almost primes,” ActaArith.(1972).
Yu. V. Linnik and A. V. Malyshev, “The application of the arithmetic of quaternions to the theory of ternary cubic forms and to the expansions of numbers as sums of cubes,” Usp. Matem. Nauk,8, No. 5(57), 3–71 (1953).
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 549–553, November, 1972.
The author is grateful to Yu. V. Linnik for valuable observations on the paper.
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Polyanskii, A.A. Representation of numbers as the sum of ternary cubic and binary quadratic forms. Mathematical Notes of the Academy of Sciences of the USSR 12, 767–769 (1972). https://doi.org/10.1007/BF01099061
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DOI: https://doi.org/10.1007/BF01099061