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Revision as of 20:12, 3 February 2010
, 20:12, 3 February 2010→Idea
Each index <math>i</math> and exponent <math>j</math> appearing in the prime factorization of a positive integer <math>n</math> is itself a positive integer, and thus has a prime factorization of its own.
Each index <math>i</math> and exponent <math>j</math> appearing in the prime factorization of a positive integer <math>n</math> is itself a positive integer, and thus has a prime factorization of its own.
Continuing with the same example, the index <math>32277</math> has the factorization <math>3 \cdot 7 \cdot 29 \cdot 53 = \text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1.</math> Taking this information together with previously known factorizations allows the following replacements to be made:
{| align="center" cellpadding="6" width="90%"
|
<math>\begin{array}{rcl}
2 & \mapsto & \text{p}_1^1
\\[6pt]
3 & \mapsto & \text{p}_2^1
\\[6pt]
7 & \mapsto & \text{p}_4^1
\\[6pt]
32277 & \mapsto & \text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1
\end{array}</math>
|}
==Riffs in Numerical Order==
==Riffs in Numerical Order==