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

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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 
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     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/}
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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/