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].
-3 x -1 x 1 = 3; 3 is a prime. A good puzzle, since it appears that if x, x+a, and x+2a are the numbers in progression, then we can prove that x divides the product, implying that the product is not prime. The trick is to notice that the product can be -x, in which case the product can be prime.
maybe not too easy?
