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Revision as of 21:02, 3 February 2010
, 21:02, 3 February 2010→Idea
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& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1} \text{p}_{\text{p}_2^1}^1 \text{p}_{\text{p}_4^1}^{\text{p}_1^1} \text{p}_{\text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1}^1
& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1} \text{p}_{\text{p}_2^1}^1 \text{p}_{\text{p}_4^1}^{\text{p}_1^1} \text{p}_{\text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1}^1
\end{array}</math>
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Continuing to replace every index and exponent with its factorization until no indices or exponents greater than <math>1</math> are left produces the following developemnt:
{| align="center" cellpadding="6" width="90%"
|
<math>\begin{array}{lll}
9876543210
& = & \text{p}_1^1 \text{p}_2^2 \text{p}_3^1 \text{p}_7^2 \text{p}_{32277}^1
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& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1} \text{p}_{\text{p}_2^1}^1 \text{p}_{\text{p}_4^1}^{\text{p}_1^1} \text{p}_{\text{p}_2^1 \text{p}_4^1 \text{p}_{10}^1 \text{p}_{16}^1}^1
\\[6pt]
& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1} \text{p}_{\text{p}_{\text{p}_1^1}^1}^1 \text{p}_{\text{p}_{\text{p}_1^2}^1}^{\text{p}_1^1} \text{p}_{\text{p}_{\text{p}_1^1}^1 \text{p}_{\text{p}_1^2}^1 \text{p}_{\text{p}_1^1 \text{p}_3^1}^1 \text{p}_{\text{p}_1^4}^1}^1
\\[6pt]
& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1} \text{p}_{\text{p}_{\text{p}_1^1}^1}^1 \text{p}_{\text{p}_{\text{p}_1^{\text{p}_1^1}}^1}^{\text{p}_1^1} \text{p}_{\text{p}_{\text{p}_1^1}^1 \text{p}_{\text{p}_1^{\text{p}_1^1}}^1 \text{p}_{\text{p}_1^1 \text{p}_{\text{p}_2^1}^1}^1 \text{p}_{\text{p}_1^{\text{p}_1^2}}^1}^1
\\[6pt]
& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1} \text{p}_{\text{p}_{\text{p}_1^1}^1}^1 \text{p}_{\text{p}_{\text{p}_1^{\text{p}_1^1}}^1}^{\text{p}_1^1} \text{p}_{\text{p}_{\text{p}_1^1}^1 \text{p}_{\text{p}_1^{\text{p}_1^1}}^1 \text{p}_{\text{p}_1^1 \text{p}_{\text{p}_{\text{p}_1^1}^1}^1}^1 \text{p}_{\text{p}_1^{\text{p}_1^{\text{p}_1^1}}}^1}^1
\end{array}</math>
\end{array}</math>
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