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Additional solutions, please (Posted on 2016-10-03) Difficulty: 3 of 5
The equation
x^2+3*y^2=x*z
has a trivial solution (not necessarily in integers) (x,y,z)=(k,0,k) for any positive k.

List all non-trivial integer triplets (x, y, z) satisfying the above equation, given z is an integer between 2000 and 3000.

No Solution Yet Submitted by Ady TZIDON    
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Solution re(2): computer solution -- final part Comment 3 of 3 |
(In reply to re: computer solution -- continued by Charlie)

1221 814 2849
2400-600 2850
450-600 2850
2400 600 2850
450 600 2850
2704-364 2851
147-364 2851
2704 364 2851
147 364 2851
1725-805 2852
1127-805 2852
2139-713 2852
713-713 2852
2484-552 2852
368-552 2852
2783-253 2852
69-253 2852
2783 253 2852
69 253 2852
2484 552 2852
368 552 2852
2139 713 2852
713 713 2852
1725 805 2852
1127 805 2852
2535-520 2855
320-520 2855
2535 520 2855
320 520 2855
1632-816 2856
1224-816 2856
2142-714 2856
714-714 2856
2550-510 2856
306-510 2856
2754-306 2856
102-306 2856
2754 306 2856
102 306 2856
2550 510 2856
306 510 2856
2142 714 2856
714 714 2856
1632 816 2856
1224 816 2856
2809-212 2857
48-212 2857
2809 212 2857
48 212 2857
1682-812 2858
1176-812 2858
1682 812 2858
1176 812 2858
1485-825 2860
1375-825 2860
2145-715 2860
715-715 2860
2640-440 2860
220-440 2860
2695-385 2860
165-385 2860
2695 385 2860
165 385 2860
2640 440 2860
220 440 2860
2145 715 2860
715 715 2860
1485 825 2860
1375 825 2860
1636-818 2863
1227-818 2863
2187-702 2863
676-702 2863
2500-550 2863
363-550 2863
2527-532 2863
336-532 2863
2527 532 2863
336 532 2863
2500 550 2863
363 550 2863
2187 702 2863
676 702 2863
1636 818 2863
1227 818 2863
2148-716 2864
716-716 2864
2148 716 2864
716 716 2864
2303-658 2867
564-658 2867
2303 658 2867
564 658 2867
2151-717 2868
717-717 2868
2151 717 2868
717 717 2868
2028-754 2869
841-754 2869
2416-604 2869
453-604 2869
2700-390 2869
169-390 2869
2793-266 2869
76-266 2869
2793 266 2869
76 266 2869
2700 390 2869
169 390 2869
2416 604 2869
453 604 2869
2028 754 2869
841 754 2869
1640-820 2870
1230-820 2870
1640 820 2870
1230 820 2870
2154-718 2872
718-718 2872
2154 718 2872
718 718 2872
2057-748 2873
816-748 2873
2652-442 2873
221-442 2873
2652 442 2873
221 442 2873
2057 748 2873
816 748 2873
2157-719 2876
719-719 2876
2157 719 2876
719 719 2876
1644-822 2877
1233-822 2877
1644 822 2877
1233 822 2877
2160-720 2880
720-720 2880
2160 720 2880
720 720 2880
1681-820 2881
1200-820 2881
1809-804 2881
1072-804 2881
2352-644 2881
529-644 2881
2752-344 2881
129-344 2881
2752 344 2881
129 344 2881
2352 644 2881
529 644 2881
1809 804 2881
1072 804 2881
1681 820 2881
1200 820 2881
1587-828 2883
1296-828 2883
2511-558 2883
372-558 2883
2511 558 2883
372 558 2883
1587 828 2883
1296 828 2883
1648-824 2884
1236-824 2884
1701-819 2884
1183-819 2884
1728-816 2884
1156-816 2884
2116-736 2884
768-736 2884
2163-721 2884
721-721 2884
2209-705 2884
675-705 2884
2523-551 2884
361-551 2884
2541-539 2884
343-539 2884
2575-515 2884
309-515 2884
2781-309 2884
103-309 2884
2800-280 2884
84-280 2884
2809-265 2884
75-265 2884
2883-31 2884
1-31 2884
2883 31 2884
1 31 2884
2809 265 2884
75 265 2884
2800 280 2884
84 280 2884
2781 309 2884
103 309 2884
2575 515 2884
309 515 2884
2541 539 2884
343 539 2884
2523 551 2884
361 551 2884
2209 705 2884
675 705 2884
2163 721 2884
721 721 2884
2116 736 2884
768 736 2884
1728 816 2884
1156 816 2884
1701 819 2884
1183 819 2884
1648 824 2884
1236 824 2884
2645-460 2885
240-460 2885
2645 460 2885
240 460 2885
1734-816 2886
1152-816 2886
1950-780 2886
936-780 2886
2592-504 2886
294-504 2886
2664-444 2886
222-444 2886
2664 444 2886
222 444 2886
2592 504 2886
294 504 2886
1950 780 2886
936 780 2886
1734 816 2886
1152 816 2886
2883-62 2887
4-62 2887
2883 62 2887
4 62 2887
1536-832 2888
1352-832 2888
1862-798 2888
1026-798 2888
2166-722 2888
722-722 2888
2432-608 2888
456-608 2888
2646-462 2888
242-462 2888
2738-370 2888
150-370 2888
2850-190 2888
38-190 2888
2850 190 2888
38 190 2888
2738 370 2888
150 370 2888
2646 462 2888
242 462 2888
2432 608 2888
456 608 2888
2166 722 2888
722 722 2888
1862 798 2888
1026 798 2888
1536 832 2888
1352 832 2888
1652-826 2891
1239-826 2891
2832-236 2891
59-236 2891
2832 236 2891
59 236 2891
1652 826 2891
1239 826 2891
2025-765 2892
867-765 2892
2169-723 2892
723-723 2892
2304-672 2892
588-672 2892
2883-93 2892
9-93 2892
2883 93 2892
9 93 2892
2304 672 2892
588 672 2892
2169 723 2892
723 723 2892
2025 765 2892
867 765 2892
2888-76 2894
6-76 2894
2888 76 2894
6 76 2894
2880-120 2895
15-120 2895
2880 120 2895
15 120 2895
1452-836 2896
1444-836 2896
2172-724 2896
724-724 2896
2700-420 2896
196-420 2896
2704-416 2896
192-416 2896
2704 416 2896
192 416 2896
2700 420 2896
196 420 2896
2172 724 2896
724 724 2896
1452 836 2896
1444 836 2896
1656-828 2898
1242-828 2898
1656 828 2898
1242 828 2898
1875-800 2899
1024-800 2899
2548-546 2899
351-546 2899
2676-446 2899
223-446 2899
2883-124 2899
16-124 2899
2883 124 2899
16 124 2899
2676 446 2899
223 446 2899
2548 546 2899
351 546 2899
1875 800 2899
1024 800 2899
2175-725 2900
725-725 2900
2175 725 2900
725 725 2900
2601-510 2901
300-510 2901
2601 510 2901
300 510 2901
2178-726 2904
726-726 2904
2178 726 2904
726 726 2904
1660-830 2905
1245-830 2905
1660 830 2905
1245 830 2905
2904-44 2906
2-44 2906
2904 44 2906
2 44 2906
2448-612 2907
459-612 2907
2448 612 2907
459 612 2907
1936-792 2908
972-792 2908
2181-727 2908
727-727 2908
2401-637 2908
507-637 2908
2883-155 2908
25-155 2908
2883 155 2908
25 155 2908
2401 637 2908
507 637 2908
2181 727 2908
727 727 2908
1936 792 2908
972 792 2908
1470-840 2910
1440-840 2910
1470 840 2910
1440 840 2910
1512-840 2912
1400-840 2912
1664-832 2912
1248-832 2912
1944-792 2912
968-792 2912
2048-768 2912
864-768 2912
2184-728 2912
728-728 2912
2312-680 2912
600-680 2912
2400-640 2912
512-640 2912
2600-520 2912
312-520 2912
2688-448 2912
224-448 2912
2744-392 2912
168-392 2912
2808-312 2912
104-312 2912
2888-152 2912
24-152 2912
2904-88 2912
8-88 2912
2904 88 2912
8 88 2912
2888 152 2912
24 152 2912
2808 312 2912
104 312 2912
2744 392 2912
168 392 2912
2688 448 2912
224 448 2912
2600 520 2912
312 520 2912
2400 640 2912
512 640 2912
2312 680 2912
600 680 2912
2184 728 2912
728 728 2912
2048 768 2912
864 768 2912
1944 792 2912
968 792 2912
1664 832 2912
1248 832 2912
1512 840 2912
1400 840 2912
2538-564 2914
376-564 2914
2538 564 2914
376 564 2914
2187-729 2916
729-729 2916
2187 729 2916
729 729 2916
2809-318 2917
108-318 2917
2809 318 2917
108 318 2917
1568-840 2918
1350-840 2918
1568 840 2918
1350 840 2918
1575-840 2919
1344-840 2919
1668-834 2919
1251-834 2919
2883-186 2919
36-186 2919
2916-54 2919
3-54 2919
2916 54 2919
3 54 2919
2883 186 2919
36 186 2919
1668 834 2919
1251 834 2919
1575 840 2919
1344 840 2919
1920-800 2920
1000-800 2920
2190-730 2920
730-730 2920
2430-630 2920
490-630 2920
2890-170 2920
30-170 2920
2890 170 2920
30 170 2920
2430 630 2920
490 630 2920
2190 730 2920
730 730 2920
1920 800 2920
1000 800 2920
2300-690 2921
621-690 2921
2300 690 2921
621 690 2921
2904-132 2922
18-132 2922
2904 132 2922
18 132 2922
1600-840 2923
1323-840 2923
1975-790 2923
948-790 2923
2523-580 2923
400-580 2923
2775-370 2923
148-370 2923
2775 370 2923
148 370 2923
2523 580 2923
400 580 2923
1975 790 2923
948 790 2923
1600 840 2923
1323 840 2923
1836-816 2924
1088-816 2924
2193-731 2924
731-731 2924
2499-595 2924
425-595 2924
2873-221 2924
51-221 2924
2873 221 2924
51 221 2924
2499 595 2924
425 595 2924
2193 731 2924
731 731 2924
1836 816 2924
1088 816 2924
2700-450 2925
225-450 2925
2700 450 2925
225 450 2925
1672-836 2926
1254-836 2926
2376-660 2926
550-660 2926
2464-616 2926
462-616 2926
2662-484 2926
264-484 2926
2662 484 2926
264 484 2926
2464 616 2926
462 616 2926
2376 660 2926
550 660 2926
1672 836 2926
1254 836 2926
2028-780 2928
900-780 2928
2196-732 2928
732-732 2928
2352-672 2928
576-672 2928
2916-108 2928
12-108 2928
2916 108 2928
12 108 2928
2352 672 2928
576 672 2928
2196 732 2928
732 732 2928
2028 780 2928
900 780 2928
1849-817 2932
1083-817 2932
2199-733 2932
733-733 2932
2500-600 2932
432-600 2932
2883-217 2932
49-217 2932
2883 217 2932
49 217 2932
2500 600 2932
432 600 2932
2199 733 2932
733 733 2932
1849 817 2932
1083 817 2932
1676-838 2933
1257-838 2933
1676 838 2933
1257 838 2933
2646-504 2934
288-504 2934
2646 504 2934
288 504 2934
1922-806 2936
1014-806 2936
2202-734 2936
734-734 2936
2450-630 2936
486-630 2936
2904-176 2936
32-176 2936
2904 176 2936
32 176 2936
2450 630 2936
486 630 2936
2202 734 2936
734 734 2936
1922 806 2936
1014 806 2936
2712-452 2938
226-452 2938
2712 452 2938
226 452 2938
1680-840 2940
1260-840 2940
1815-825 2940
1125-825 2940
2205-735 2940
735-735 2940
2535-585 2940
405-585 2940
2625-525 2940
315-525 2940
2835-315 2940
105-315 2940
2880-240 2940
60-240 2940
2880 240 2940
60 240 2940
2835 315 2940
105 315 2940
2625 525 2940
315 525 2940
2535 585 2940
405 585 2940
2205 735 2940
735 735 2940
1815 825 2940
1125 825 2940
1680 840 2940
1260 840 2940
2888-228 2942
54-228 2942
2888 228 2942
54 228 2942
2916-162 2943
27-162 2943
2916 162 2943
27 162 2943
2208-736 2944
736-736 2944
2208 736 2944
736 736 2944
1500-850 2945
1445-850 2945
2480-620 2945
465-620 2945
2565-570 2945
380-570 2945
2940-70 2945
5-70 2945
2940 70 2945
5 70 2945
2565 570 2945
380 570 2945
2480 620 2945
465 620 2945
1500 850 2945
1445 850 2945
1684-842 2947
1263-842 2947
2100-770 2947
847-770 2947
2704-468 2947
243-468 2947
2883-248 2947
64-248 2947
2883 248 2947
64 248 2947
2704 468 2947
243 468 2947
2100 770 2947
847 770 2947
1684 842 2947
1263 842 2947
1617-847 2948
1331-847 2948
2211-737 2948
737-737 2948
2673-495 2948
275-495 2948
2816-352 2948
132-352 2948
2816 352 2948
132 352 2948
2673 495 2948
275 495 2948
2211 737 2948
737 737 2948
1617 847 2948
1331 847 2948
2724-454 2951
227-454 2951
2724 454 2951
227 454 2951
2214-738 2952
738-738 2952
2214 738 2952
738 738 2952
1728-840 2953
1225-840 2953
1728 840 2953
1225 840 2953
1688-844 2954
1266-844 2954
2058-784 2954
896-784 2954
2738-444 2954
216-444 2954
2904-220 2954
50-220 2954
2904 220 2954
50 220 2954
2738 444 2954
216 444 2954
2058 784 2954
896 784 2954
1688 844 2954
1266 844 2954
1587-851 2956
1369-851 2956
2217-739 2956
739-739 2956
2700-480 2956
256-480 2956
2809-371 2956
147-371 2956
2809 371 2956
147 371 2956
2700 480 2956
256 480 2956
2217 739 2956
739 739 2956
1587 851 2956
1369 851 2956
2000-800 2960
960-800 2960
2220-740 2960
740-740 2960
2420-660 2960
540-660 2960
2940-140 2960
20-140 2960
2940 140 2960
20 140 2960
2420 660 2960
540 660 2960
2220 740 2960
740 740 2960
2000 800 2960
960 800 2960
1692-846 2961
1269-846 2961
1692 846 2961
1269 846 2961
1539-855 2964
1425-855 2964
1764-840 2964
1200-840 2964
1875-825 2964
1089-825 2964
1911-819 2964
1053-819 2964
2223-741 2964
741-741 2964
2496-624 2964
468-624 2964
2523-609 2964
441-609 2964
2601-561 2964
363-561 2964
2736-456 2964
228-456 2964
2793-399 2964
171-399 2964
2883-279 2964
81-279 2964
2916-216 2964
48-216 2964
2925-195 2964
39-195 2964
2925 195 2964
39 195 2964
2916 216 2964
48 216 2964
2883 279 2964
81 279 2964
2793 399 2964
171 399 2964
2736 456 2964
228 456 2964
2601 561 2964
363 561 2964
2523 609 2964
441 609 2964
2496 624 2964
468 624 2964
2223 741 2964
741 741 2964
1911 819 2964
1053 819 2964
1875 825 2964
1089 825 2964
1764 840 2964
1200 840 2964
1539 855 2964
1425 855 2964
2166-760 2966
800-760 2966
2166 760 2966
800 760 2966
1863-828 2967
1104-828 2967
1863 828 2967
1104 828 2967
1696-848 2968
1272-848 2968
2226-742 2968
742-742 2968
2650-530 2968
318-530 2968
2862-318 2968
106-318 2968
2862 318 2968
106 318 2968
2650 530 2968
318 530 2968
2226 742 2968
742 742 2968
1696 848 2968
1272 848 2968
2187-756 2971
784-756 2971
2187 756 2971
784 756 2971
2229-743 2972
743-743 2972
2229 743 2972
743 743 2972
1521-858 2973
1452-858 2973
1521 858 2973
1452 858 2973
1700-850 2975
1275-850 2975
1700 850 2975
1275 850 2975
1800-840 2976
1176-840 2976
2232-744 2976
744-744 2976
2592-576 2976
384-576 2976
2904-264 2976
72-264 2976
2904 264 2976
72 264 2976
2592 576 2976
384 576 2976
2232 744 2976
744 744 2976
1800 840 2976
1176 840 2976
1573-858 2977
1404-858 2977
2209-752 2977
768-752 2977
2352-700 2977
625-700 2977
2748-458 2977
229-458 2977
2748 458 2977
229 458 2977
2352 700 2977
625 700 2977
2209 752 2977
768 752 2977
1573 858 2977
1404 858 2977
2400-680 2978
578-680 2978
2400 680 2978
578 680 2978
2304-720 2979
675-720 2979
2304 720 2979
675 720 2979
2235-745 2980
745-745 2980
2235 745 2980
745 745 2980
2156-770 2981
825-770 2981
2156 770 2981
825 770 2981
1704-852 2982
1278-852 2982
1704 852 2982
1278 852 2982
2052-798 2983
931-798 2983
2116-782 2983
867-782 2983
2512-628 2983
471-628 2983
2883-310 2983
100-310 2983
2883 310 2983
100 310 2983
2512 628 2983
471 628 2983
2116 782 2983
867 782 2983
2052 798 2983
931 798 2983
1734-850 2984
1250-850 2984
2238-746 2984
746-746 2984
2646-546 2984
338-546 2984
2888-304 2984
96-304 2984
2888 304 2984
96 304 2984
2646 546 2984
338 546 2984
2238 746 2984
746 746 2984
1734 850 2984
1250 850 2984
2940-210 2985
45-210 2985
2940 210 2985
45 210 2985
2900-290 2987
87-290 2987
2900 290 2987
87 290 2987
2241-747 2988
747-747 2988
2241 747 2988
747 747 2988
1708-854 2989
1281-854 2989
2028-806 2989
961-806 2989
2401-686 2989
588-686 2989
2541-616 2989
448-616 2989
2700-510 2989
289-510 2989
2800-420 2989
189-420 2989
2928-244 2989
61-244 2989
2928 244 2989
61 244 2989
2800 420 2989
189 420 2989
2700 510 2989
289 510 2989
2541 616 2989
448 616 2989
2401 686 2989
588 686 2989
2028 806 2989
961 806 2989
1708 854 2989
1281 854 2989
2760-460 2990
230-460 2990
2760 460 2990
230 460 2990
2916-270 2991
75-270 2991
2916 270 2991
75 270 2991
2244-748 2992
748-748 2992
2244 748 2992
748 748 2992
1968-820 2993
1025-820 2993
1968 820 2993
1025 820 2993
1536-864 2994
1458-864 2994
1536 864 2994
1458 864 2994
1712-856 2996
1284-856 2996
2247-749 2996
749-749 2996
2675-535 2996
321-535 2996
2889-321 2996
107-321 2996
2889 321 2996
107 321 2996
2675 535 2996
321 535 2996
2247 749 2996
749 749 2996
1712 856 2996
1284 856 2996
2025-810 2997
972-810 2997
2025 810 2997
972 810 2997
2250-750 3000
750-750 3000
2250 750 3000
750 750 3000


  Posted by Charlie on 2016-10-03 18:10:37
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