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International
Tables for Crystallography Volume A1 Symmetry relations between space groups Edited by Hans Wondratschek and Ulrich Müller © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A1. ch. 3.1, pp. 428-433
https://doi.org/10.1107/97809553602060000547 Chapter 3.1. Guide to the tables
a
Fachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany |
Footnotes
1
If the sum of two square numbers is a prime number p, then it is ![[p= 2]](/teximages/a1ach3o1/a1ach3o1fi20.svg)
or ![[p=4n+1]](/teximages/a1ach3o1/a1ach3o1fi39.svg)
, and every prime number of this type can be expressed as such a sum. Index number restrictions of this kind occur among isomorphic subgroups of certain tetragonal space groups. A similar relation occurring among trigonal and hexagonal space groups concerns prime numbers ![[p=q^2-qr+r^2]](/teximages/a1ach3o1/a1ach3o1fi40.svg)
; ![[p=3]](/teximages/a1ach1o5/a1ach1o5fi1380.svg)
or ![[p=6n+1]](/teximages/a1ach3o1/a1ach3o1fi42.svg)
always holds for integer q, r and every prime number can be expressed by such a sum. For details, see Müller & Brelle (1995![[link]](/graphics/greenarr.gif)
).
or , and every prime number of this type can be expressed as such a sum. Index number restrictions of this kind occur among isomorphic subgroups of certain tetragonal space groups. A similar relation occurring among trigonal and hexagonal space groups concerns prime numbers ; or always holds for integer q, r and every prime number can be expressed by such a sum. For details, see Müller & Brelle (1995).