Geodesic
Pythagorean ratios in arithmetic progression, part i. three Pythagorean ratios
Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 395-407

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

Let {a, b} designate the Pythagorean ratio (a2 - b2)/2ab between the sides of a rational right angled triangle. This paper studies the circumstances in which Pythagorean ratios can occupy consecutive places in an arithmetic progression. Part I deals with sets of three such ratios, while Part II discusses sets of four ratios. 
Pythagorean ratios in arithmetic progression, part i. three Pythagorean ratios. Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 395-407. doi: 10.1017/S0017089500009988
@misc{10_1017_S0017089500009988,
     title = {Pythagorean ratios in arithmetic progression, part i. three {Pythagorean} ratios},
     journal = {Glasgow mathematical journal},
     pages = {395--407},
     year = {1993},
     volume = {35},
     number = {3},
     doi = {10.1017/S0017089500009988},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009988/}
}
TY  - JOUR
TI  - Pythagorean ratios in arithmetic progression, part i. three Pythagorean ratios
JO  - Glasgow mathematical journal
PY  - 1993
SP  - 395
EP  - 407
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009988/
DO  - 10.1017/S0017089500009988
ID  - 10_1017_S0017089500009988
ER  - 
%0 Journal Article
%T Pythagorean ratios in arithmetic progression, part i. three Pythagorean ratios
%J Glasgow mathematical journal
%D 1993
%P 395-407
%V 35
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009988/
%R 10.1017/S0017089500009988
%F 10_1017_S0017089500009988

[1] 1.Cohn, J. H. E., Squares in arithmetical progressions. Math. Scand. 52 (1983), 5–19. Google Scholar | DOI

[2] 2.Dickson, L. E., History of the Theory of Numbers, vol. 2, Diophantine analysis (Carnegie Institute, Washington 1920) 172–174. Google Scholar

[3] 3.Guy, R. K., Unsolved Problems in Number Theory (Springer Verlag, New York and Berlin, 1981). Google Scholar | DOI

[4] 4.Lagrange, J. and Leech, J., Two triads of squares. Maths. Comp. 46 (1986), 751–758. Google Scholar | DOI

[5] 5.Leech, J., The rational cuboid revisited. Amer. Math. Monthly 84 (1977), 518–533. Google Scholar | DOI

Cité par Sources :