Ternary parallelogram scales are MOS substitution: Difference between revisions
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Claim: ''k''<sub>'''w'''</sub> has order ''n'' in {{nowrap|ℤ/''mn''ℤ.}} | Claim: ''k''<sub>'''w'''</sub> has order ''n'' in {{nowrap|ℤ/''mn''ℤ.}} | ||
Proof: The order cannot be less than ''n'', lest we have {{nowrap|φ((0, ''uk''<sub>'''w'''</sub>)) {{=}} 0}} for some {{nowrap|0 < ''u'' < ''n'',}} contradicting injectivity of φ within a fundamental domain. | Proof: The order cannot be less than ''n'', lest we have {{nowrap|φ((0, ''uk''<sub>'''w'''</sub>)) {{=}} 0}} for some {{nowrap|0 < ''u'' < ''n'',}} contradicting injectivity of φ within a fundamental domain (following from previous lemma). | ||
Assume that the order is ''N'' > ''n''. | Assume that the order is ''N'' > ''n''. | ||