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 One and Only by Sanjay)

While the Random House dictionary defines prime number

a positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded

mathematicians would almost always exclude 1, rather than just "often". Otherwise prime factorizations would not be unique. For example, 15 = 3 x 5 becomes 15=3x5 or 15=3x5x1 or 15 = 3x5x1x1 or 15=3x5x1x1x1, etc.

Posted by Charlie on 2003-06-03 08:48:16