N=(abcabd) is a 6-digit number with d-c=1.

FIND N, given it is an even square.

Rem: (abcabd) denotes chaining (= concatenation), not a product

DEFDBL A-Z
CLS
FOR abc = 100 TO 998
  s$ = LTRIM$(STR$(abc))
  IF RIGHT$(s$, 1) < "9" THEN
    abcabd = abc * 1001 + 1
    sr = INT(SQR(abcabd) + .5)
    IF sr * sr = abcabd AND abcabd MOD 2 = 0 THEN PRINT abcabd
  END IF
NEXT abc

finds

 183184
 715716

Posted by Charlie on 2013-01-18 12:11:10