Determine all possible integer pair(s) (C, D) that satisfy this equation:

C² - 3CD = C - D

Firstly to FrankM.  What precludes C not being "0"?  A simple substitution of that value necessarily renders D to "0".

The following program listing:......

 CLS

 PRINT "Increase from 0 to 100"
 FOR c = 0 TO 100
  FOR d = 0 TO 100
   IF (c * c - 3 * c * d = c - d) THEN PRINT c, d
  NEXT
 NEXT
PRINT "both negatives"
 FOR c = -100 TO 0 STEP 1
  FOR d = -100 TO 0 STEP 1
    IF (c * c - 3 * c * d = c - d) THEN PRINT c, d
  NEXT
 NEXT
PRINT "C pos D neg"
 FOR c = 0 TO 100
  FOR d = -100 TO 0 STEP 1
    IF (c * c - 3 * c * d = c - d) THEN PRINT c, d
  NEXT
 NEXT
PRINT "C neg D pos"
 FOR c = -100 TO 0 STEP 1
  FOR d = 0 TO 100
    IF (c * c - 3 * c * d = c - d) THEN PRINT c, d
  NEXT
 NEXT

............produced this as a screen output:

Increase from 0 to 100
 0             0
 1             0
both negatives
 0             0
C pos D neg
 0             0
 1             0
C neg D pos
 0             0


To look for integer pairs I chose the respective possible pairings of positive and negative within the |100| range certain of the outcome anyway.

Posted by brianjn on 2008-04-15 23:34:25