Geodesic
Involutions Associated With Sums of two Squares
Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 18 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In 1984 D.R. Heath-Brown constructed two involutions from which a new and simple proof of Fermat's theorem on the decomposition of a prime $p\equiv 1\pmod 4$ as a sum of two squares was derived. An algorithm based on the composition of the two involutions is constructed for the decomposition of $p$, and the method can also be used for the factorisations of suitable composite numbers. The process corresponds to the continued fraction expansion of a reduced quadratic irrational related to $\sqrt p$, and the period of the composite map is the sum of the relevant partial quotients.
Classification : 11A51 11Y05
Keywords: Fermat's two square theorem, involutions, periods factorisation, continued fractions 
@article{PIM_1996_N_S_59_73_a2,
     author = {P. Shiu},
     title = {Involutions {Associated} {With} {Sums} of two {Squares}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {18 },
     publisher = {mathdoc},
     volume = {_N_S_59},
     number = {73},
     year = {1996},
     zbl = {0884.11008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a2/}
}
TY  - JOUR
AU  - P. Shiu
TI  - Involutions Associated With Sums of two Squares
JO  - Publications de l'Institut Mathématique
PY  - 1996
SP  - 18 
VL  - _N_S_59
IS  - 73
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a2/
LA  - en
ID  - PIM_1996_N_S_59_73_a2
ER  - 
%0 Journal Article
%A P. Shiu
%T Involutions Associated With Sums of two Squares
%J Publications de l'Institut Mathématique
%D 1996
%P 18 
%V _N_S_59
%N 73
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a2/
%G en
%F PIM_1996_N_S_59_73_a2
P. Shiu. Involutions Associated With Sums of two Squares. Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 18 . http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a2/