Geodesic
On the representation of numbers by binary biquadratic forms
Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 415-422 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper it is proved that if the rank of the equation $ax^4+bx^2y^2+cy^4=kz^2$ over the field $R(1)$ does not exceed unity, and if $k$ is not divisible by any fourth power and is relatively prime to the discriminant, then, provided that $\frac{(b^2-4ac)}{\max\{|a|,|c|\}}$ is sufficiently large relative to $k$, the equation $ax^4+bx^2y^2+cy^4=k$ does not have more than three positive integer solutions. Bibliography: 10 titles. 
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     author = {V. A. Dem'yanenko},
     title = {On~the representation of numbers by binary biquadratic forms},
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V. A. Dem'yanenko. On the representation of numbers by binary biquadratic forms. Sbornik. Mathematics, Tome 9 (1969) no. 3, pp. 415-422. http://geodesic.mathdoc.fr/item/SM_1969_9_3_a8/

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[9] V. A. Demyanenko, “Otsenka ostatochnogo chlena v formule Teita”, Matem. zametki, 3:3 (1968), 271–278

[10] E. Gekke, Lektsii po teorii algebraicheskikh chisel, Gostekhizdat, M., 1940