2. Results of computation

In case of -100 ≤ n ≤ -1 where 0 ≤ (x,y,z) ≤ 1000

n	x	y	z
-4	1	2	-6
-4	-1	3	6
-10	1	3	-12
-10	-1	4	12
-11	-1	6	10
-12	4	35	-84
-18	1	4	-20
-18	-1	5	20
-18	-40	315	616
-19	-3	14	66
-20	-1	10	15
-25	1	15	-40
-28	1	5	-30
-28	-1	6	30
-28	-21	165	560
-29	-12	77	364
-31	-1	15	21
-32	-15	136	440
-39	-1	12	33
-40	1	6	-42
-40	-1	7	42
-44	-1	21	28
-48	12	65	-572
-52	5	18	-230
-54	1	7	-56
-54	-1	8	56
-59	-1	28	36
-59	-2	21	114
-59	-6	35	406
-67	-15	348	740
-69	-3	68	156
-70	1	8	-72
-70	-1	9	72
-70	9	275	-900
-76	-1	36	45
-76	-3	20	255
-85	-4	133	228
-88	1	9	-90
-88	-1	10	90
-89	-1	20	76
-91	-3	102	187
-95	-1	45	55

In case of 1 ≤ n ≤ 100, 0 ≤ where (x,y,z) ≤ 1000

(Solutions for n=0,1 are omitted)

n	x	y	z
11	1	2	3
11	3	-28	60
14	2	3	10
15	1	3	6
15	12	-165	340
18	2	3	15
18	2	10	15
26	1	6	14
29	2	-15	78
30	10	77	165
31	1	-12	44
34	1	6	21
35	3	10	65
37	2	-35	110
52	5	-464	720
55	1	14	35
57	6	-35	435
59	2	15	85
63	5	119	170
64	1	-40	104
67	5	-68	420
71	4	-33	348
73	1	-20	95
74	5	22	270
84	2	-78	247
85	5	-138	570
86	3	-336	592
100	5	-56	595

Parametrized solution

n = -(k-1)(k+2)
   (x, y, z) = (1, k, -k(k+1)), (-1, k+1, -k(k+1))

lcm(1, k, -k(k+1))=k(k+1)=lcm(-1, k+1, -k(k+1))

so, these two solutions are dual.