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import math
 
 
def find(n):
    # max of x can be sqrt of n
    n1 = int(math.ceil(math.sqrt(n)))
    lst = []
 
    for i in range(1, n1):
        for j in range(i + 1, n1):
 
            if i**2 + j**2 >= n:
                break
 
            tz = int(math.sqrt(n - i**2 - j**2))
            if tz ** 2 == n - i**2 - j**2:
                a = [i, j, tz]
                lst.append(a)
    return lst
 
print find(12345678)

Success #stdin #stdout 0.13s 67964KB

stdin

Standard input is empty

stdout

[[1, 371, 3494], [1, 2141, 2786], [1, 2786, 2141], [1, 3494, 371], [5, 1097, 3338], [5, 3338, 1097], [7, 1390, 3227], [7, 2027, 2870], [7, 2870, 2027], [7, 3227, 1390], [13, 847, 3410], [13, 1265, 3278], [13, 3278, 1265], [13, 3410, 847], [14, 851, 3409], [14, 3409, 851], [15, 1422, 3213], [15, 2322, 2637], [15, 2637, 2322], [15, 3213, 1422], [18, 1323, 3255], [18, 3255, 1323], [19, 1871, 2974], [19, 2974, 1871], [23, 2218, 2725], [23, 2725, 2218], [27, 582, 3465], [27, 3465, 582], [29, 2014, 2879], [29, 2879, 2014], [34, 491, 3479], [34, 2351, 2611], [34, 2611, 2351], [34, 3479, 491], [41, 1426, 3211], [41, 1594, 3131], [41, 3131, 1594], [41, 3211, 1426], [50, 377, 3493], [50, 3493, 377], [55, 1958, 2917], [55, 2917, 1958], [58, 1717, 3065], [58, 3065, 1717], [61, 1391, 3226], [61, 3226, 1391], [63, 147, 3510], [63, 3510, 147], [65, 698, 3443], [65, 982, 3373], [65, 1478, 3187], [65, 1738, 3053], [65, 3053, 1738], [65, 3187, 1478], [65, 3373, 982], [65, 3443, 698], [67, 2065, 2842], [67, 2842, 2065], [70, 1987, 2897], [70, 2897, 1987], [71, 166, 3509], [71, 3509, 166], [77, 1057, 3350], [77, 3350, 1057], [82, 1265, 3277], [82, 3277, 1265], [83, 1633, 3110], [83, 3110, 1633], [85, 617, 3458], [85, 1303, 3262], [85, 3262, 1303], [85, 3458, 617], [91, 1354, 3241], [91, 3241, 1354], [106, 1591, 3131], [106, 3131, 1591], [107, 265, 3502], [107, 2150, 2777], [107, 2777, 2150], [107, 3502, 265], [110, 1847, 2987], [110, 2987, 1847], [113, 1678, 3085], [113, 1910, 2947], [113, 2947, 1910], [113, 3085, 1678], [117, 342, 3495], [117, 810, 3417], [117, 1770, 3033], [117, 2295, 2658], [117, 2658, 2295], [117, 3033, 1770], [117, 3417, 810], [117, 3495, 342], [118, 1385, 3227], [118, 1973, 2905], [118, 2905, 1973], [118, 3227, 1385], [121, 134, 3509], [121, 901, 3394], [121, 3394, 901], [121, 3509, 134], [125, 257, 3502], [125, 518, 3473], [125, 3473, 518], [125, 3502, 257], [126, 531, 3471], [126, 3471, 531], [127, 1405, 3218], [127, 1990, 2893], [127, 2893, 1990], [127, 3218, 1405], [131, 191, 3506], [131, 3506, 191], [133, 1658, 3095], [133, 2183, 2750], [133, 2750, 2183], [133, 3095, 1658], [134, 3509, 121], [142, 1433, 3205], [142, 2395, 2567], [142, 2567, 2395], [142, 3205, 1433], [147, 1638, 3105], [147, 3105, 1638], [147, 3510, 63], [149, 454, 3481], [149, 3481, 454], [154, 281, 3499], [154, 869, 3401], [154, 1991, 2891], [154, 2089, 2821], [154, 2821, 2089], [154, 2891, 1991], [154, 3401, 869], [154, 3499, 281], [155, 1622, 3113], [155, 3113, 1622], [162, 1797, 3015], [162, 2415, 2547], [162, 2547, 2415], [162, 3015, 1797], [166, 701, 3439], [166, 3439, 701], [166, 3509, 71], [170, 397, 3487], [170, 3487, 397], [177, 1107, 3330], [177, 3330, 1107], [181, 646, 3449], [181, 3449, 646], [187, 775, 3422], [187, 1178, 3305], [187, 3305, 1178], [187, 3422, 775], [190, 1693, 3073], [190, 3073, 1693], [191, 659, 3446], [191, 1261, 3274], [191, 1741, 3046], [191, 3046, 1741], [191, 3274, 1261], [191, 3446, 659], [191, 3506, 131], [198, 957, 3375], [198, 3375, 957], [202, 595, 3457], [202, 835, 3407], [202, 1745, 3043], [202, 2093, 2815], [202, 2815, 2093], [202, 3043, 1745], [202, 3407, 835], [202, 3457, 595], [203, 2038, 2855], [203, 2338, 2615], [203, 2615, 2338], [203, 2855, 2038], [205, 2417, 2542], [205, 2542, 2417], [209, 1309, 3254], [209, 1891, 2954], [209, 2954, 1891], [209, 3254, 1309], [214, 2261, 2681], [214, 2681, 2261], [215, 1717, 3058], [215, 2437, 2522], [215, 2522, 2437], [215, 3058, 1717], [217, 1525, 3158], [217, 3158, 1525], [225, 243, 3498], [225, 3498, 243], [226, 421, 3481], [226, 769, 3421], [226, 3421, 769], [226, 3481, 421], [231, 981, 3366], [231, 1611, 3114], [231, 3114, 1611], [231, 3366, 981], [238, 245, 3497], [238, 3497, 245], [239, 2179, 2746], [239, 2746, 2179], [243, 3498, 225], [245, 3497, 238], [247, 1510, 3163], [247, 3163, 1510], [253, 350, 3487], [253, 1462, 3185], [253, 3185, 1462], [253, 3487, 350], [254, 1969, 2899], [254, 2899, 1969], [257, 950, 3373], [257, 3373, 950], [257, 3502, 125], [258, 1755, 3033], [258, 3033, 1755], [261, 1161, 3306], [261, 2151, 2766], [261, 2766, 2151], [261, 3306, 1161], [265, 1237, 3278], [265, 3278, 1237], [265, 3502, 107], [271, 509, 3466], [271, 3466, 509], [274, 289, 3491], [274, 601, 3451], [274, 3451, 601], [274, 3491, 289], [278, 1745, 3037], [278, 3037, 1745], [279, 714, 3429], [279, 3429, 714], [281, 2459, 2494], [281, 2494, 2459], [281, 3499, 154], [287, 797, 3410], [287, 1030, 3347], [287, 3347, 1030], [287, 3410, 797], [289, 499, 3466], [289, 2029, 2854], [289, 2339, 2606], [289, 2606, 2339], [289, 2854, 2029], [289, 3466, 499], [289, 3491, 274], [293, 2105, 2798], [293, 2798, 2105], [301, 986, 3359], [301, 1519, 3154], [301, 3154, 1519], [301, 3359, 986], [302, 1435, 3193], [302, 2393, 2555], [302, 2555, 2393], [302, 3193, 1435], [307, 2225, 2702], [307, 2702, 2225], [309, 1449, 3186], [309, 3186, 1449], [313, 1765, 3022], [313, 3022, 1765], [314, 379, 3479], [314, 2071, 2821], [314, 2821, 2071], [314, 3479, 379], [322, 655, 3437], [322, 3437, 655], [323, 2182, 2735], [323, 2735, 2182], [325, 1463, 3178], [325, 3178, 1463], [331, 601, 3446], [331, 1609, 3106], [331, 3106, 1609], [331, 3446, 601], [338, 953, 3365], [338, 3365, 953], [341, 814, 3401], [341, 3401, 814], [342, 3495, 117], [350, 2057, 2827], [350, 2827, 2057], [350, 3487, 253], [355, 2063, 2822], [355, 2822, 2063], [358, 1765, 3017], [358, 2417, 2525], [358, 2525, 2417], [358, 3017, 1765], [362, 1955, 2897], [362, 2897, 1955], [370, 2003, 2863], [370, 2863, 2003], [371, 766, 3409], [371, 3409, 766], [371, 3494, 1], [373, 407, 3470], [373, 1975, 2882], [373, 2882, 1975], [373, 3470, 407], [377, 875, 3382], [377, 2030, 2843], [377, 2282, 2645], [377, 2645, 2282], [377, 2843, 2030], [377, 3382, 875], [377, 3493, 50], [378, 855, 3387], [378, 945, 3363], [378, 1635, 3087], [378, 1863, 2955], [378, 2955, 1863], [378, 3087, 1635], [378, 3363, 945], [378, 3387, 855], [379, 3479, 314], [386, 1301, 3241], [386, 3241, 1301], [390, 1233, 3267], [390, 3267, 1233], [397, 3487, 170], [401, 694, 3421], [401, 1766, 3011], [401, 3011, 1766], [401, 3421, 694], [406, 521, 3451], [406, 3451, 521], [407, 2123, 2770], [407, 2770, 2123], [407, 3470, 373], [410, 917, 3367], [410, 1183, 3283], [410, 3283, 1183], [410, 3367, 917], [414, 2199, 2709], [414, 2709, 2199], [415, 1517, 3142], [415, 3142, 1517], [419, 586, 3439], [419, 3439, 586], [421, 3481, 226], [422, 2087, 2795], [422, 2795, 2087], [441, 1686, 3051], [441, 3051, 1686], [443, 698, 3415], [443, 3415, 698], [447, 1350, 3213], [447, 3213, 1350], [450, 1017, 3333], [450, 2043, 2823], [450, 2823, 2043], [450, 3333, 1017], [454, 3481, 149], [457, 902, 3365], [457, 3365, 902], [463, 778, 3395], [463, 1778, 2995], [463, 2995, 1778], [463, 3395, 778], [467, 1567, 3110], [467, 3110, 1567], [469, 1394, 3191], [469, 2089, 2786], [469, 2786, 2089], [469, 3191, 1394], [471, 891, 3366], [471, 3366, 891], [474, 1251, 3249], [474, 3249, 1251], [477, 2175, 2718], [477, 2718, 2175], [478, 2263, 2645], [478, 2645, 2263], [481, 2234, 2669], [481, 2669, 2234], [490, 1733, 3017], [490, 2353, 2563], [490, 2563, 2353], [490, 3017, 1733], [491, 3479, 34], [497, 2387, 2530], [497, 2530, 2387], [498, 765, 3393], [498, 1143, 3285], [498, 3285, 1143], [498, 3393, 765], [499, 1154, 3281], [499, 3281, 1154], [499, 3466, 289], [502, 1643, 3065], [502, 3065, 1643], [503, 1205, 3262], [503, 1237, 3250], [503, 3250, 1237], [503, 3262, 1205], [505, 2002, 2843], [505, 2843, 2002], [506, 1381, 3191], [506, 2129, 2749], [506, 2749, 2129], [506, 3191, 1381], [509, 1601, 3086], [509, 3086, 1601], [509, 3466, 271], [513, 1878, 2925], [513, 2925, 1878], [518, 3473, 125], [521, 2086, 2779], [521, 2219, 2674], [521, 2674, 2219], [521, 2779, 2086], [521, 3451, 406], [523, 1210, 3257], [523, 1370, 3193], [523, 3193, 1370], [523, 3257, 1210], [527, 1507, 3130], [527, 1885, 2918], [527, 2918, 1885], [527, 3130, 1507], [531, 639, 3414], [531, 3414, 639], [531, 3471, 126], [547, 562, 3425], [547, 3425, 562], [553, 2437, 2470], [553, 2470, 2437], [554, 1841, 2941], [554, 2941, 1841], [555, 1062, 3303], [555, 1287, 3222], [555, 3222, 1287], [555, 3303, 1062], [557, 1610, 3073], [557, 3073, 1610], [562, 1345, 3197], [562, 3197, 1345], [562, 3425, 547], [565, 1433, 3158], [565, 3158, 1433], [566, 929, 3341], [566, 1099, 3289], [566, 3289, 1099], [566, 3341, 929], [567, 2283, 2610], [567, 2610, 2283], [569, 709, 3394], [569, 1541, 3106], [569, 3106, 1541], [569, 3394, 709], [579, 1206, 3249], [579, 1521, 3114], [579, 3114, 1521], [579, 3249, 1206], [582, 2205, 2673], [582, 2673, 2205], [582, 3465, 27], [583, 1870, 2917], [583, 2917, 1870], [586, 719, 3389], [586, 1349, 3191], [586, 2311, 2581], [586, 2581, 2311], [586, 3191, 1349], [586, 3389, 719], [586, 3439, 419], [587, 2375, 2522], [587, 2522, 2375], [594, 1419, 3159], [594, 3159, 1419], [595, 1217, 3242], [595, 3242, 1217], [595, 3457, 202], [601, 3446, 331], [601, 3451, 274], [602, 1715, 3007], [602, 1975, 2843], [602, 2843, 1975], [602, 3007, 1715], [617, 842, 3355], [617, 3355, 842], [617, 3458, 85], [619, 1666, 3031], [619, 1799, 2954], [619, 2954, 1799], [619, 3031, 1666], [621, 2241, 2634], [621, 2634, 2241], [622, 1763, 2975], [622, 2975, 1763], [630, 2337, 2547], [630, 2547, 2337], [631, 1541, 3094], [631, 3094, 1541], [635, 1913, 2878], [635, 2102, 2743], [635, 2743, 2102], [635, 2878, 1913], [637, 847, 3350], [637, 1697, 3010], [637, 3010, 1697], [637, 3350, 847], [639, 2106, 2739], [639, 2739, 2106], [639, 3414, 531], [643, 2002, 2815], [643, 2815, 2002], [646, 3449, 181], [653, 785, 3362], [653, 3362, 785], [655, 3437, 322], [657, 1470, 3123], [657, 1875, 2898], [657, 2898, 1875], [657, 3123, 1470], [659, 974, 3311], [659, 3311, 974], [659, 3446, 191], [663, 1710, 2997], [663, 2997, 1710], [665, 1378, 3163], [665, 1477, 3118], [665, 3118, 1477], [665, 3163, 1378], [666, 1359, 3171], [666, 3171, 1359], [670, 2263, 2603], [670, 2603, 2263], [671, 1006, 3299], [671, 3299, 1006], [677, 982, 3305], [677, 1930, 2857], [677, 2857, 1930], [677, 3305, 982], [679, 994, 3301], [679, 3301, 994], [685, 2287, 2578], [685, 2578, 2287], [686, 1301, 3191], [686, 3191, 1301], [694, 1199, 3229], [694, 3229, 1199], [694, 3421, 401], [698, 3415, 443], [698, 3443, 65], [701, 1346, 3169], [701, 3169, 1346], [701, 3439, 166], [707, 1550, 3073], [707, 2402, 2465], [707, 2465, 2402], [707, 3073, 1550], [709, 1639, 3026], [709, 3026, 1639], [709, 3394, 569], [713, 1045, 3278], [713, 3278, 1045], [714, 3429, 279], [715, 1783, 2942], [715, 2942, 1783], [719, 2221, 2626], [719, 2626, 2221], [719, 3389, 586], [721, 1501, 3094], [721, 1834, 2909], [721, 2909, 1834], [721, 3094, 1501], [722, 1085, 3263], [722, 1745, 2963], [722, 2963, 1745], [722, 3263, 1085], [729, 2226, 2619], [729, 2331, 2526], [729, 2526, 2331], [729, 2619, 2226], [733, 1583, 3050], [733, 3050, 1583], [734, 961, 3299], [734, 1979, 2809], [734, 2809, 1979], [734, 3299, 961], [741, 1449, 3114], [741, 3114, 1449], [743, 1675, 2998], [743, 2998, 1675], [749, 2134, 2689], [749, 2689, 2134], [758, 2095, 2717], [758, 2417, 2435], [758, 2435, 2417], [758, 2717, 2095], [763, 1478, 3095], [763, 1847, 2890], [763, 2890, 1847], [763, 3095, 1478], [765, 3393, 498], [766, 2009, 2779], [766, 2779, 2009], [766, 3409, 371], [769, 3421, 226], [770, 1007, 3277], [770, 3277, 1007], [775, 3422, 187], [778, 3395, 463], [785, 2098, 2707], [785, 2707, 2098], [785, 3362, 653], [791, 811, 3326], [791, 3326, 811], [793, 1202, 3205], [793, 1930, 2827], [793, 2827, 1930], [793, 3205, 1202], [797, 3410, 287], [798, 2043, 2745], [798, 2745, 2043], [802, 2107, 2695], [802, 2695, 2107], [803, 863, 3310], [803, 2113, 2690], [803, 2690, 2113], [803, 3310, 863], [810, 3417, 117], [811, 1094, 3239], [811, 1591, 3026], [811, 1721, 2954], [811, 2954, 1721], [811, 3026, 1591], [811, 3239, 1094], [811, 3326, 791], [814, 1121, 3229], [814, 3229, 1121], [814, 3401, 341], [815, 2093, 2702], [815, 2702, 2093], [821, 986, 3271], [821, 3271, 986], [825, 1638, 2997], [825, 2997, 1638], [835, 3407, 202], [839, 1349, 3134], [839, 3134, 1349], [842, 883, 3295], [842, 1633, 2995], [842, 1867, 2855], [842, 2855, 1867], [842, 2995, 1633], [842, 3295, 883], [842, 3355, 617], [847, 3350, 637], [847, 3410, 13], [851, 3409, 14], [853, 1862, 2855], [853, 2855, 1862], [854, 2339, 2479], [854, 2401, 2419], [854, 2419, 2401], [854, 2479, 2339], [855, 2133, 2658], [855, 2658, 2133], [855, 3387, 378], [859, 1954, 2791], [859, 2294, 2519], [859, 2519, 2294], [859, 2791, 1954], [862, 1405, 3103], [862, 3103, 1405], [863, 925, 3278], [863, 1510, 3053], [863, 1622, 2995], [863, 2995, 1622], [863, 3053, 1510], [863, 3278, 925], [863, 3310, 803], [866, 1051, 3239], [866, 2311, 2501], [866, 2501, 2311], [866, 3239, 1051], [869, 1001, 3254], [869, 1666, 2969], [869, 2234, 2569], [869, 2569, 2234], [869, 2969, 1666], [869, 3254, 1001], [869, 3401, 154], [873, 1770, 2907], [873, 2907, 1770], [875, 3382, 377], [877, 1007, 3250], [877, 1105, 3218], [877, 3218, 1105], [877, 3250, 1007], [881, 2269, 2534], [881, 2534, 2269], [883, 1583, 3010], [883, 3010, 1583], [883, 3295, 842], [887, 2053, 2710], [887, 2710, 2053], [891, 1254, 3159], [891, 3159, 1254], [891, 3366, 471], [895, 1178, 3187], [895, 3187, 1178], [898, 965, 3257], [898, 1693, 2945], [898, 2945, 1693], [898, 3257, 965], [901, 2119, 2654], [901, 2654, 2119], [901, 3394, 121], [902, 3365, 457], [917, 1550, 3017], [917, 3017, 1550], [917, 3367, 410], [918, 2205, 2577], [918, 2577, 2205], [925, 1958, 2767], [925, 2767, 1958], [925, 3278, 863], [929, 2029, 2714], [929, 2714, 2029], [929, 3341, 566], [938, 2353, 2435], [938, 2435, 2353], [945, 1107, 3198], [945, 1782, 2877], [945, 2877, 1782], [945, 3198, 1107], [945, 3363, 378], [950, 3373, 257], [953, 1675, 2938], [953, 2938, 1675], [953, 3365, 338], [954, 2361, 2421], [954, 2421, 2361], [957, 2070, 2673], [957, 2673, 2070], [957, 3375, 198], [958, 1133, 3185], [958, 1525, 3017], [958, 3017, 1525], [958, 3185, 1133], [961, 1966, 2749], [961, 2749, 1966], [961, 3299, 734], 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