kill(all)$

van=facebook.com/LearningCalculus$

A + B + C + D = 2013$
A - B         =    1$
    B - C     =    3$
        C - D =    2$

M: matrix
(
    [  1,  1,  1,  1],
    [  1, -1,  0,  0],
    [  0,  1, -1,  0],
    [  0,  0,  1, -1]
)$

b:matrix([2013],[1],[3],[2])$

score: first(fullratsimp(linsolve_by_lu(M,b)));

count:0$ printf(true, "Answer")$
for j: 1 thru first(score[1]) do
    if primep(j)                  and
       mod(first(score[1]),j) > 0 and
       mod(first(score[2]),j) > 0 and
       mod(first(score[3]),j) > 0 and
       mod(first(score[4]),j) > 0 then
       (
           count:count+1,

           printf(true, "~4d, ", j),
           if mod(count, 10) = 0 then printf(true, "~%Answer")
           
       )$