Determine the total number of ways in which 111 can be written as a sum of three distinct nonzero integers which are in geometric sequence.

Prove that there are no others.

The program checks for all possible sets of three distinct positive integers. Cases of negative, positive, negative or positive, negative, positive have not been considered here:

FOR a = 1 TO 111 / 3
FOR b = a + 1 TO (111 - a) / 2
c = 111 - a - b
IF c > b THEN
    IF a * c = b * b THEN PRINT a; b; c: ct = ct + 1
END IF
NEXT
NEXT

PRINT ct

It finds 2 solutions in which all the integers are positive:

1  10  100
27  36  48

Posted by Charlie on 2013-08-07 12:28:09