Geodesic
Pairs of Theonian Triangles with Common Area
Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 729-734.

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

We study the properties of pairs of triangles with integer sides whose common area is the square of a natural number.
Keywords: Theonian triangle, Heronian triangle, basic Theonian and Heronian triangle. 
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S. Sh. Kozhegel'dinov. Pairs of Theonian Triangles with Common Area. Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 729-734. http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a7/

[1] L. E. Dickson, History of the Theory of Numbers, v. II, Diophantine Analysis, Chelsea Publ., New York, NY, 1966 | MR | Zbl

[2] D. Singmaster, “Heronian triangles”, Math. Spectrum, 11:2 (1978), 58–59

[3] S. Sh. Kozhegeldinov, “Otyskanie osnovnykh geronovykh treugolnikov (GT)”, Izv. AN Respubliki Kazakhstan. Ser. fiz.-matem., 1992, no. 3, 48–51 | MR

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

[5] S. Sh. Kozhegeldinov, “K resheniyu sistemy uravnenii Gerona”, Matem. zametki, 69:5 (2001), 688–698 | MR | Zbl

[6] S. Sh. Kozhegeldinov, “Dvukhtysyacheletnii barer vzyat”, Izbrannye stati i doklady, Nauchnoe izdanie, Almaty, 2001

[7] S. Sh. Kozhegeldinov, “O tianovykh treugolnikakh”, Respubl. konf. “Teoriya chisel i ee prilozheniya”, Tezisy dokladov, Tashkent, 1990, 62

[8] S. Sh. Kozhegeldinov, “K voprosu o tianovykh treugolnikakh (TT)”, Matem. zametki, 53:5 (1993), 155–157 | MR | Zbl

[9] S. Sh. Kozhegeldinov, “Ob osnovnykh tianovykh treugolnikakh”, Mezhdunar. konf. “Sovremennye problemy teorii chisel” (Tula), Tezisy dokladov, 1993

[10] S. Sh. Kozhegeldinov, “Ob osnovnykh tianovykh treugolnikakh”, Matem. zametki, 61:4 (1997), 561–569 | MR | Zbl

[11] S. Sh. Kozhegeldinov, Obschie formuly geronovykh treugolnikov i ikh chastnye sluchai. II, Dep. v VINITI, No 8-V90

[12] S. Sh. Kozhegeldinov, “Tianovy treugolniki s obschei ploschadyu”, Mezhdunar. konf. “Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya” posvyaschennaya 80-letiyu prof. T. I. Amanova. Sbornik dokladov, Semipalatinsk, 2003, 203–206

[13] S. Sh. Kozhegeldinov, Problema 20, Preprint AN BSSR, No 35, 1990

[14] R. A. Melter, W. E. Briggs, D. Pagus, “Problems and Solutions. Advanced Problems: 6628–6630”, Amer. Math. Monthly, 97:4 (1990), 350 ; R. A. Melter, C. R. Maderer, J. H. Steelman, J. Buddenhagen, “Problems and Solutions. Solutions of Advanced Problems: 6628”, Amer. Math. Monthly, 98:8 (1991), 772–774 | DOI | MR | DOI | MR

[15] I. Vidav, “Heronovi trikotniki in diofantsue enacbe”, Obzornik Mat. Fiz., 38:1 (1991), 1–7 | MR | Zbl