2. Results of computation

nxyz
-412-6
-4-136
-1013-12
-10-1412
-11-1610
-12435-84
-1814-20
-18-1520
-18-40315616
-19-31466
-20-11015
-25115-40
-2815-30
-28-1630
-28-21165560
-29-1277364
-31-11521
-32-15136440
-39-11233
-4016-42
-40-1742
-44-12128
-481265-572
-52518-230
-5417-56
-54-1856
-59-12836
-59-221114
-59-635406
-67-15348740
-69-368156
-7018-72
-70-1972
-709275-900
-76-13645
-76-320255
-85-4133228
-8819-90
-88-11090
-89-12076
-91-3102187
-95-14555

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

(Solutions for n=0,1 are omitted)
nxyz
11123
113-2860
142310
15136
1512-165340
182315
1821015
261614
292-1578
301077165
311-1244
341621
3531065
372-35110
525-464720
5511435
576-35435
5921585
635119170
641-40104
675-68420
714-33348
731-2095
74522270
842-78247
855-138570
863-336592
1005-56595

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.

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima