Do there exist three integers in Arithmetic Progression whose product is prime ? If Yes, then what are the three integers and if No, then why ?

[Note: The numbers: x1, x2, x3, x4, x5, x6,........ are said to be in Arithmetic Progression if (x2 - x1) = (x3 - x2) = (x4 - x3) = (x5 - x4) = ........ and so on].

(In reply to re(2): One and Only by Sanjay)

I would say never can 1 be included as a prime number. First of all, if any problem wanted to include 1, just say "non-composite" instead of prime.

Including the prime factorization argument, you could also state that a prime number has to have exactly 2 factors (which is the definition I heard, although it might not be right), and since 1 only has 1 factor, it isn't prime.

I also would point out that in order to be in arithmetic progression, the sequence would need to progress (get larger or smaller). I don't know about this idea for this problem, because of the Note: definition given.

I think this is an interesting solution though. If the progression arguement is thrown out, why not -1,-1,-1? -1 has two factors, -1 and 1, and is prime. (Are we saying also that 0 is not prime?)

Posted by Gamer on 2003-06-03 12:41:33