COMMENT ⊗   VALID 00003 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	\example 
C00006 00003	The program generates values for {\tt A, B, C, D} in the order:
C00008 ENDMK
C⊗;
\example 
Write a PASCAL program to find four positive integers  $A < B < C < D$  for
which $B↑3 + C↑3 = A↑3 + D↑3$.  In other words, find a positive integer that
can be represented two ways as the sum of two cubes.  The program below finds
such an integer (one exists), but does not necessarily find the smallest one.

\startcode
PROGRAM SUMOFCUBES ( OUTPUT ) ;
(* THIS PROGRAM FINDS FOUR INTEGERS: 0 < A < B < C < D
   FOR WHICH   A*A*A + D*D*D = B*B*B + C*C*C  *)
VAR     A, B, C, D :  INTEGER ;
BEGIN
A := 1 ;
B := 2 ;
C := 3 ;
D := 4 ;
WHILE  A*A*A + D*D*D <> B*B*B +C*C*C DO
    IF A < B - 1  THEN  A := A + 1
    ELSE
        BEGIN
        A := 1 ;
        IF B < C - 1  THEN  B := B + 1
        ELSE 
            BEGIN
            B := 2 ;
            IF C < D + 1  THEN  C := C + 1
            ELSE
                BEGIN
                C := 3 ;
                D := D + 1 
                END
            END
        END ;
WRITELN ( A, D, B, C )
END.
\endcode
\vfill\eject
The program generates values for {\tt A, B, C, D} in the order:

\dtable{\hfill#\hfill\qquad⊗\hfill#\hfill\qquad⊗\hfill#\hfill\qquad⊗\hfill#\hfill\cr
{\tt A}⊗{\tt B}⊗{\tt C}⊗{\tt D}\cr
1⊗2⊗3⊗4\cr
1⊗2⊗3⊗5\cr
1⊗2⊗4⊗5\cr
1⊗3⊗4⊗5\cr
2⊗3⊗4⊗5\cr
1⊗2⊗3⊗6\cr
1⊗2⊗4⊗6\cr
1⊗3⊗4⊗6\cr
2⊗3⊗4⊗6\cr
1⊗2⊗5⊗6\cr
1⊗3⊗5⊗6\cr
2⊗3⊗5⊗6\cr
1⊗4⊗5⊗6\cr
2⊗4⊗5⊗6\cr
3⊗4⊗5⊗6\cr
1⊗2⊗3⊗7\cr
⊗etc.⊗⊗\cr
}%end dtable

The program, upon finding $A↑3 + D↑3 ≠ B↑3 + C↑3$, increases the first of
$A$, $B$, $C$, $D$ that can be increased without becoming equal to the next
variable; it sets all the earlier variables back to their initial values.