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Subject: "https://www.cut-the-knot.org/do_you_know/ProductAndSum.shtml"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #628
Reading Topic #628
Bill McEachen
guest
 May-20-07, 02:34 PM (EST)
 
"https://www.cut-the-knot.org/do_you_know/ProductAndSum.shtml"
 
   I definitely could be wrong, but doesn't the stronger statement apply for summing:
every composite can be expressed as the sum of a lone prime factor?
obviously even composit's use 2, numbers ending in "5" use 5, but the rest do too? eg 39=13+13+13. It's a fancy way of noting that every composite can be expressed as the product of exactly 2 odd numbers, at least one of them a prime. just post the first counterexample, thanks
billymac_AT_ excite.com


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alexbadmin
Charter Member
2011 posts		 May-20-07, 03:32 PM (EST)
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1. "RE: ProductAndSum.shtml"
In response to message #0
 
   >I definitely could be wrong, but doesn't the stronger
>statement apply for summing:
>every composite can be expressed as the sum of a lone prime
>factor?
>obviously even composit's use 2, numbers ending in "5" use
>5, but the rest do too? eg 39=13 13 13. It's a fancy way of
>noting that every composite can be expressed as the product
>of exactly 2 odd numbers, at least one of them a prime.
>just post the first counterexample, thanks
>billymac_AT_ excite.com

This not very exciting problem is not about either sums or products but about sums having as many summands as products have factors.


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