Geodesic
The al-Husayn Equation $x^4+y^2=z^2$
Matematičeskie zametki, Tome 89 (2011) no. 3, pp. 365-377.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the set of all natural solutions of the equation $x^4+y^2=z^2$, obtain general formulas describing all such solutions, and prove their equivalence.
Keywords: the al-Husayn equation $x^4+y^2=z^2$, Pythagorean triangle, arithmetical function.
Mots-clés : Diophantine equation 
@article{MZM_2011_89_3_a5,
     author = {S. Sh. Kozhegel'dinov},
     title = {The {al-Husayn} {Equation} $x^4+y^2=z^2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {365--377},
     publisher = {mathdoc},
     volume = {89},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a5/}
}
TY  - JOUR
AU  - S. Sh. Kozhegel'dinov
TI  - The al-Husayn Equation $x^4+y^2=z^2$
JO  - Matematičeskie zametki
PY  - 2011
SP  - 365
EP  - 377
VL  - 89
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a5/
LA  - ru
ID  - MZM_2011_89_3_a5
ER  - 
%0 Journal Article
%A S. Sh. Kozhegel'dinov
%T The al-Husayn Equation $x^4+y^2=z^2$
%J Matematičeskie zametki
%D 2011
%P 365-377
%V 89
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a5/
%G ru
%F MZM_2011_89_3_a5
S. Sh. Kozhegel'dinov. The al-Husayn Equation $x^4+y^2=z^2$. Matematičeskie zametki, Tome 89 (2011) no. 3, pp. 365-377. http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a5/

[1] A. O. Gelfond, Reshenie uravnenii v tselykh chislakh, Populyarnye lektsii po matematike, 8, Nauka, M., 1978 | MR | Zbl

[2] V. Serpinskii, Pifagorovy treugolniki, Uchpedgiz, M., 1959 | MR | Zbl

[3] A. Beiker, Vvedenie v teoriyu chisel, Vysheishaya shkola, Minsk, 1995 | MR | Zbl

[4] I. G. Bashmakova, E. I. Slavutin, Istoriya diofantova analiza ot Diofanta do Ferma, Nauka, M., 1984 | MR | Zbl

[5] Diofant Aleksandriiskii, Arifmetika i kniga o mnogougolnykh chislakh, Nauka, M., 1974 | MR | Zbl

[6] P. Ferma, Issledovaniya po teorii chisel i diofantovu analizu, Nauka, M., 1992 | MR | Zbl

[7] L. E. Dickson, History of the Theory of Numbers, v. 2, Diophantine Analysis, Carnegie Institution of Washington, New York, 1920 | MR | Zbl

[8] L. J. Mordell, Diophantine Equations, Pure Appl. Math., 30, Academic Press, New York, 1969 | MR | Zbl

[9] S. Sh. Kozhegeldinov, Nekotorye elementy teorii diofantovykh uravnenii v uprazhneniyakh i zadachakh, Prometei, M., 1993

[10] S. Sh. Kozhegeldinov, “Ob osnovnykh geronovykh treugolnikakh”, Matem. zametki, 55:2 (1994), 72–79 | MR | Zbl

[11] S. Sh. Kozhegeldinov, “Ob ekvivalentnosti obschikh formul osnovnykh reshenii odnogo diofantova uravneniya”, III Respublikanskaya konferentsiya, posvyaschennaya pamyati professora T. I. Amanova (1923–1978), Sbornik dokladov. Chast 2, KarGU, Karaganda, 1998, 129–135

[12] S. Sh. Kozhegeldinov, Nekotorye klassicheskie diofantovy uravneniya ot trekh i bolee peremennykh: v 5-ti tomakh, v. 1, Novosibirsk, 2002; т. 2, Алматы, 2004; т. 3, Алматы, 2006; т. 4, Семей, 2008; т. 5, Семей, 2008

[13] S. Sh. Kozhegeldinov, “O reshenii uravnenii v naturalnykh chislakh”, Mezhvuzovskaya konferentsiya, posvyaschennaya 70-letiyu so dnya rozhdeniya professora T. I. Amanova, Tezisy dokladov, SGPI im. Shakarima, Semipalatinsk, 1993, 17–19

[14] S. Sh. Kozhegeldinov, “Ob issledovanii arifmeticheskikh funktsii”, II Mezhdunarodnaya konferentsiya “Algebraicheskie, veroyatnostnye, geometricheskie, kombinatornye i funktsionalnye metody v teorii chisel”, Tezisy dokladov, VGU, Voronezh, 1995, 85

[15] S. Sh. Kozhegeldinov, “Ob odnom diofantovom uravnenii”, III Mezhdunarodnaya konferentsiya “Sovremennye problemy teorii chisel i ee prilozheniya”, Tezisy dokladov, TGPU, Tula, 1996, 77