Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 625003811 - Original comment: ** |
Wikispaces>TallKite **Imported revision 625004165 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-17 14: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-17 14:37:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>625004165</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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if n = |b|, then |z| = n/|b| = 1, and from the earlier proof, n = 1 | if n = |b|, then |z| = n/|b| = 1, and from the earlier proof, n = 1 | ||
if n = 1, |z|·|b| = 1, therefore |b| = 1, and n = |b| | if n = 1, |z|·|b| = 1, therefore |b| = 1, and n = |b| | ||
Therefore multigens like M9/3 or M3/ | Therefore multigens like M9/3 or M3/4 never occur | ||
Therefore a and b must be coprime, otherwise M/n could be simplified by GCD (a,b) | Therefore a and b must be coprime, otherwise M/n could be simplified by GCD (a,b) | ||
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if n = |b|, then |z| = n/|b| = 1, and from the earlier proof, n = 1<br /> | if n = |b|, then |z| = n/|b| = 1, and from the earlier proof, n = 1<br /> | ||
if n = 1, |z|·|b| = 1, therefore |b| = 1, and n = |b|<br /> | if n = 1, |z|·|b| = 1, therefore |b| = 1, and n = |b|<br /> | ||
Therefore multigens like M9/3 or M3/ | Therefore multigens like M9/3 or M3/4 never occur<br /> | ||
Therefore a and b must be coprime, otherwise M/n could be simplified by GCD (a,b)<br /> | Therefore a and b must be coprime, otherwise M/n could be simplified by GCD (a,b)<br /> | ||
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