Geodesic
Diophantine equations related to quasicrystals: A note
Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 3, pp. 477-480 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give the general solution of three Diophantine equations in the ring of integers of the algebraic number field $\mathbf{Q}\bigl[\sqrt{5}\,\bigr]$. These equations are related to the problem of determining the minimum distance in quasicrystals with fivefold symmetry. 
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E. Pelantova; A. M. Perelomov. Diophantine equations related to quasicrystals: A note. Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 3, pp. 477-480. http://geodesic.mathdoc.fr/item/TMF_1998_115_3_a10/

[1] H. Hasse, Number theory, Springer-Verlag, New York, 1980 | MR | Zbl

[2] Z. Masáková, J. Patera, E. Pelantová, On the minimal distance in quasicrystal, Submitted for publication

[3] L. Chen, R. V. Moody, J. Patera, “Non-crystallographic root systems”, Quasicrystals and discrete geometry, Fields Inst. Commun., ed. J. Patera (to appear) | MR