{
 "cells": [
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   "cell_type": "code",
   "execution_count": 1,
   "id": "9907ace0-b025-49e4-b73a-a2ba242b6478",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ENV[\"LINES\"] = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2f9810da-186f-43da-835d-a84046ccbde8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100-element Vector{Tuple{Int64, Int64, Int64}}:\n",
       " (3, 4, 5)\n",
       " (5, 12, 13)\n",
       " (7, 24, 25)\n",
       " (8, 15, 17)\n",
       " (9, 40, 41)\n",
       " (11, 60, 61)\n",
       " (12, 35, 37)\n",
       " (13, 84, 85)\n",
       " (15, 112, 113)\n",
       " (16, 63, 65)\n",
       " (17, 144, 145)\n",
       " (19, 180, 181)\n",
       " (20, 21, 29)\n",
       " (20, 99, 101)\n",
       " (21, 220, 221)\n",
       " (23, 264, 265)\n",
       " (24, 143, 145)\n",
       " (25, 312, 313)\n",
       " (27, 364, 365)\n",
       " (28, 45, 53)\n",
       " (28, 195, 197)\n",
       " (29, 420, 421)\n",
       " (31, 480, 481)\n",
       " (32, 255, 257)\n",
       " (33, 56, 65)\n",
       " (33, 544, 545)\n",
       " (35, 612, 613)\n",
       " (36, 77, 85)\n",
       " (36, 323, 325)\n",
       " (37, 684, 685)\n",
       " (39, 80, 89)\n",
       " (39, 760, 761)\n",
       " (40, 399, 401)\n",
       " (41, 840, 841)\n",
       " (43, 924, 925)\n",
       " (44, 117, 125)\n",
       " (44, 483, 485)\n",
       " (45, 1012, 1013)\n",
       " (47, 1104, 1105)\n",
       " (48, 55, 73)\n",
       " (48, 575, 577)\n",
       " (49, 1200, 1201)\n",
       " (51, 140, 149)\n",
       " (51, 1300, 1301)\n",
       " (52, 165, 173)\n",
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       " (57, 176, 185)\n",
       " (57, 1624, 1625)\n",
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       " (60, 221, 229)\n",
       " (60, 899, 901)\n",
       " (61, 1860, 1861)\n",
       " (63, 1984, 1985)\n",
       " (64, 1023, 1025)\n",
       " (65, 72, 97)\n",
       " (65, 2112, 2113)\n",
       " (67, 2244, 2245)\n",
       " (68, 285, 293)\n",
       " (68, 1155, 1157)\n",
       " (69, 260, 269)\n",
       " (69, 2380, 2381)\n",
       " (71, 2520, 2521)\n",
       " (72, 1295, 1297)\n",
       " (73, 2664, 2665)\n",
       " (75, 308, 317)\n",
       " (75, 2812, 2813)\n",
       " (76, 357, 365)\n",
       " (76, 1443, 1445)\n",
       " (77, 2964, 2965)\n",
       " (79, 3120, 3121)\n",
       " (80, 1599, 1601)\n",
       " (81, 3280, 3281)\n",
       " (83, 3444, 3445)\n",
       " (84, 187, 205)\n",
       " (84, 437, 445)\n",
       " (84, 1763, 1765)\n",
       " (85, 132, 157)\n",
       " (85, 3612, 3613)\n",
       " (87, 416, 425)\n",
       " (87, 3784, 3785)\n",
       " (88, 105, 137)\n",
       " (88, 1935, 1937)\n",
       " (89, 3960, 3961)\n",
       " (91, 4140, 4141)\n",
       " (92, 525, 533)\n",
       " (92, 2115, 2117)\n",
       " (93, 476, 485)\n",
       " (93, 4324, 4325)\n",
       " (95, 168, 193)\n",
       " (95, 4512, 4513)\n",
       " (96, 247, 265)\n",
       " (96, 2303, 2305)\n",
       " (97, 4704, 4705)\n",
       " (99, 4900, 4901)\n",
       " (100, 621, 629)\n",
       " (100, 2499, 2501)"
      ]
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 100\n",
    "[(a, b, isqrt(a^2+b^2)) for a in 3:n for b in a+1:a^2÷2\n",
    "    if gcd(a, b) == 1 && a^2 + b^2 == isqrt(a^2 + b^2)^2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f71ef859-f22f-43de-b946-1a8fdc6a56c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51-element Vector{Tuple{Int64, Int64, Int64}}:\n",
       " (8, 15, 17)\n",
       " (12, 35, 37)\n",
       " (16, 63, 65)\n",
       " (20, 21, 29)\n",
       " (20, 99, 101)\n",
       " (24, 143, 145)\n",
       " (28, 45, 53)\n",
       " (28, 195, 197)\n",
       " (32, 255, 257)\n",
       " (33, 56, 65)\n",
       " (36, 77, 85)\n",
       " (36, 323, 325)\n",
       " (39, 80, 89)\n",
       " (40, 399, 401)\n",
       " (44, 117, 125)\n",
       " (44, 483, 485)\n",
       " (48, 55, 73)\n",
       " (48, 575, 577)\n",
       " (51, 140, 149)\n",
       " (52, 165, 173)\n",
       " (52, 675, 677)\n",
       " (56, 783, 785)\n",
       " (57, 176, 185)\n",
       " (60, 91, 109)\n",
       " (60, 221, 229)\n",
       " (60, 899, 901)\n",
       " (64, 1023, 1025)\n",
       " (65, 72, 97)\n",
       " (68, 285, 293)\n",
       " (68, 1155, 1157)\n",
       " (69, 260, 269)\n",
       " (72, 1295, 1297)\n",
       " (75, 308, 317)\n",
       " (76, 357, 365)\n",
       " (76, 1443, 1445)\n",
       " (80, 1599, 1601)\n",
       " (84, 187, 205)\n",
       " (84, 437, 445)\n",
       " (84, 1763, 1765)\n",
       " (85, 132, 157)\n",
       " (87, 416, 425)\n",
       " (88, 105, 137)\n",
       " (88, 1935, 1937)\n",
       " (92, 525, 533)\n",
       " (92, 2115, 2117)\n",
       " (93, 476, 485)\n",
       " (95, 168, 193)\n",
       " (96, 247, 265)\n",
       " (96, 2303, 2305)\n",
       " (100, 621, 629)\n",
       " (100, 2499, 2501)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 100\n",
    "[(a, b, isqrt(a^2+b^2)) for a in 3:n for b in a+1:max(n, a^2÷2)\n",
    "    if gcd(a, b) == 1 && a^2 + b^2 == isqrt(a^2 + b^2)^2 && b != a^2÷2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21802ed7-8736-42ae-b7d8-58dd687eaafe",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "formats": "ipynb,auto:hydrogen"
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