SOLUTION: three consecutive numbers whose sum is equal to their products.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: three consecutive numbers whose sum is equal to their products.       Log On


   

Question 464461: three consecutive numbers whose sum is equal to their products.
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1, 2 & 3 is the only example I know.
Ooooh, -1, 0 and 1 too.

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
-3,-2,-1 works as well. But then {-1,0,1}, {1,2,3} and {-3,-2,-1} are the only sets of three consecutive integers satisfying this property, because if we were to write it algebraically (e.g. (a-1) + a + (a+1) = (a-1)a(a+1), 3a = a(a-1)(a+1)) we would get a cubic, which has at most three distinct solutions for a.