Delta-N ratio: Difference between revisions
factorization of delta-N ratios |
→Properties: an explicit product formula |
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* 4/1 = (16/13) (13/10) (10/7) (7/4). | * 4/1 = (16/13) (13/10) (10/7) (7/4). | ||
Also, if you factorize like this into ''K'' factors, then each of them into ''L'' factors, you get the same as if you directly factored into ''K L'' factors. | Also, if you factorize like this into ''K'' factors, then each of them into ''L'' factors, you get the same as if you directly factored into ''K L'' factors. | ||
:The general formula for this factorization is <math>\displaystyle\prod_{i = 1}^K \frac {K A + i N} {K A + (i - 1) N} = \frac {A + N} A</math>. | |||
[[Wikipedia:Størmer's theorem|Størmer's theorem]] can be extended to show that for each prime limit ''p'' and each degree of epimericity ''n'', there are only finitely many ''p''-limit ratios with degree of epimoricity less than or equal to ''n''. | [[Wikipedia:Størmer's theorem|Størmer's theorem]] can be extended to show that for each prime limit ''p'' and each degree of epimericity ''n'', there are only finitely many ''p''-limit ratios with degree of epimoricity less than or equal to ''n''. | ||