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Summing or Multiplying (Posted on 2006-08-21) Difficulty: 4 of 5
123 is a peculiar integer, because 1+2+3=1*2*3. 1412 is also peculiar, since 1+4+1+2=1*4*1*2.

A simple question: are there infinitely many such numbers?

A not so simple question: if so, are there such numbers for ANY number of digits?

See The Solution Submitted by e.g.    
Rating: 4.2500 (8 votes)

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Some Thoughts re: With a program | Comment 5 of 20 |
(In reply to With a program by Joe)

If we are to find a 24-digit peculiar number, the most "non-one" digits could be 5, since 2^6-12 is more than 24. Just running the program for a=2 to 9, b=2 to 9, up to e=2 to 9, would suffice to disprove the idea that there are peculiar numbers of any length.
  Posted by Federico Kereki on 2006-08-21 19:08:01

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