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].

Going strictly by the definition of Arithmetic Progression provided in the problem 1,1,1 is a solution.

x1=1,x2=1,x3=1
x2-x1=0
x3-x2=0
So, (x2-x1)=(x3-x2)
Therefore 1,1,1 constitutes an Arithmetic Progression.

Also, 1*1*1=1, which is a prime number.

Posted by Sanjay on 2003-06-03 07:00:49