On Unique-Factorization Combinatorics via the Pascal Triangle

by Frank C. Fung ( 1st published in October, 2012. )

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Section V - Formulating { Category X Numbers } with 1 prime-number

Summary for the Section :

• In this Section , we shall attempt to answer this question :

  QUESTION :

  • How many distinct-and-different { Category X Composite Numbers } can we formulate
    • if we were to start-out with exactly 1 prime-number ;

    with the 2 special conditions being that :

    • the one-and-only prime-numbers must appear at-least-once as a prime-factor of the formulated-number [ N ] ,

      and

    • repetition of the prime-number as a prime-factor of the formulated-number [ N ] is allowed .

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Finding the Answer :

• The answer here is quite obvious :
  • [ 1 ]

  And the formulated { Category X Composite Number } is simply :

  • the [ prime-number ] raised to the 10th-power .

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Total Count for [ 1 Prime-Numbers ] :

• The Total Count for originally starting-out with 1 prime-number is therefore :
  • [ 1 ]

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go to the next section : Section VI - Formulating [ Category X Numbers ] with 2 prime-numbers

go to the last section : Section IV - Setting up for the Calculations to follow in the next 10 Sections

return to the Unique-Factorization Combinatorics HomePage

Original dated 2012-10-08