Geodesic
Explicit Solutions of Pyramidal Diophantine Equations
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 177-184

Voir la notice de l'article provenant de la source Cambridge University Press

Let P m, k denote the set of pyramidal numbers 1.1 The question has been asked whether there exist elements p, q, r in Pm, k such that p+q = r or, as the problem is usually posed, 1.2 The case k=2 has been studied by Sierpinski [6] and Khatri [3]; the case k=3 by Oppenheim [4] and Segal [5]; recently Fraenkel [2] has generalized (1.1) to the larger set 1.3 
Bernstein, Leon. Explicit Solutions of Pyramidal Diophantine Equations. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 177-184. doi: 10.4153/CMB-1972-032-6
@article{10_4153_CMB_1972_032_6,
     author = {Bernstein, Leon},
     title = {Explicit {Solutions} of {Pyramidal} {Diophantine} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {177--184},
     year = {1972},
     volume = {15},
     number = {2},
     doi = {10.4153/CMB-1972-032-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-032-6/}
}
TY  - JOUR
AU  - Bernstein, Leon
TI  - Explicit Solutions of Pyramidal Diophantine Equations
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 177
EP  - 184
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-032-6/
DO  - 10.4153/CMB-1972-032-6
ID  - 10_4153_CMB_1972_032_6
ER  - 
%0 Journal Article
%A Bernstein, Leon
%T Explicit Solutions of Pyramidal Diophantine Equations
%J Canadian mathematical bulletin
%D 1972
%P 177-184
%V 15
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-032-6/
%R 10.4153/CMB-1972-032-6
%F 10_4153_CMB_1972_032_6

[1] 1. Leon, Bernstein, A probability function for partitions, Amer. Math. Monthly (1968), 882-886. Google Scholar

Leon, Bernstein, New infinite classes of periodic Jacobi-Perron algorithms, Pacific J. Math., (3) 16 (1966), 439-469. Google Scholar

Leon, Bernstein, The generalized Pellian equation, Trans. Amer. Math. Soc. (1) 127 (1967), 76-89. Google Scholar

[2] 2. Fraenkel, Aviezri S., Diophantine equations involving generalized triangular and tetrahedral numbers (to appear). Google Scholar

[3] 3. Khatri, M. N., Triangular numbers andpythagorean triangles, Scripta Math. 21 (1955), 94. Google Scholar

[4] 4. Oppenheim, A., On the diophantine equation x3 + y3 + z 3 = x + y + z, Proc. Amer. Math. Soc. 16 (1965), 148-153. Google Scholar

Oppenheim, A., On the diophantine equation x 3 +y 3 + z 3 ?px +py?qz , Publ. Faculté D'electrotech. Univ. Belgrade, Ser. Math. Physique, No. 230-No. 241 (1968), 33-35. Google Scholar

[5] 5. Segal, S. L., A note on pyramidal numbers, Amer. Math. Monthly (1962), 637-638. Google Scholar

[6] 6. Sierpinski, W., Elementary theory of numbers, Translated from Polish by A. Hulamiki, Oxford Pergamon Press, 1964. Google Scholar

Cité par Sources :