Pythagoras Checker.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9, 40] [[0, 0], [1, 1], [1, 3], [2, 1], [2, 2]] 4\n",
      "10\n",
      "[133, 156] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[273, 136] [[0, 0], [1, 2], [2, 2]] 2\n",
      "[189, 340] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[33, 544] [[0, 0], [2, 2], [3, 1]] 2\n",
      "20\n",
      "[399, 40] [[0, 0], [2, 2], [2, 4]] 2\n",
      "[561, 400] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[57, 1624] [[0, 0], [1, 1], [2, 2]] 2\n",
      "30\n",
      "[399, 1600] [[0, 0], [2, 1], [2, 2]] 2\n",
      "[1173, 1036] [[0, 0], [1, 1], [2, 2]] 2\n",
      "40\n",
      "[1581, 820] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[89, 3960] [[0, 0], [2, 1], [2, 2]] 2\n",
      "50\n",
      "[1513, 3816] [[0, 0], [1, 1], [2, 2]] 2\n",
      "60\n",
      "[3577, 1464] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[3901, 2340] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[2461, 5460] [[0, 0], [1, 1], [2, 2]] 2\n",
      "70\n",
      "[973, 9636] [[0, 0], [1, 1], [2, 2]] 2\n",
      "80\n",
      "[7029, 2380] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[5289, 7480] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[5617, 8544] [[0, 0], [1, 1], [2, 2]] 2\n",
      "90\n",
      "[1309, 17460] [[0, 0], [1, 1], [2, 2]] 2\n",
      "100\n",
      "[9717, 4444] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[5797, 17004] [[0, 0], [1, 1], [2, 2]] 2\n",
      "110\n",
      "[12513, 3616] [[0, 0], [1, 1], [2, 2]] 2\n",
      "120\n",
      "[12921, 13000] [[0, 0], [1, 1], [2, 2]] 2\n",
      "130\n",
      "[4369, 32880] [[0, 0], [1, 1], [2, 2]] 2\n",
      "140\n",
      "[20701, 5220] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[20349, 7540] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[18601, 17880] [[0, 0], [1, 1], [2, 2]] 2\n",
      "150\n",
      "[12549, 34540] [[0, 0], [1, 1], [2, 2]] 2\n",
      "160\n",
      "[337, 56784] [[0, 0], [1, 1], [2, 2]] 2\n",
      "170\n",
      "[2359, 56760] [[0, 0], [2, 1], [2, 2]] 2\n",
      "[26329, 20760] [[0, 0], [1, 1], [2, 2]] 2\n",
      "180\n",
      "[32361, 7240] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[29869, 24420] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[15729, 50320] [[0, 0], [1, 1], [2, 2]] 2\n",
      "190\n",
      "[22849, 46320] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[37909, 11820] [[0, 0], [1, 1], [2, 2]] 2\n",
      "200\n",
      "[31621, 41820] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[8901, 74620] [[0, 0], [1, 1], [2, 2]] 2\n",
      "210\n",
      "220\n",
      "[48357, 9724] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[12741, 83980] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[47817, 31144] [[0, 0], [1, 1], [2, 2]] 2\n",
      "230\n",
      "[37389, 60580] [[0, 0], [1, 1], [2, 2]] 2\n",
      "240\n",
      "[58065, 1928] [[0, 0], [1, 2], [2, 2]] 2\n",
      "[34977, 73264] [[0, 0], [1, 1], [2, 2]] 2\n",
      "250\n",
      "[64893, 17476] [[0, 0], [1, 1], [2, 2]] 2\n",
      "260\n",
      "[69649, 12720] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[57229, 60420] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[66277, 41964] [[0, 0], [1, 1], [2, 2]] 2\n",
      "270\n",
      "[57129, 77560] [[0, 0], [1, 1], [2, 2]] 2\n",
      "280\n",
      "[34861, 118020] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[39421, 121380] [[0, 0], [1, 1], [2, 2]] 2\n",
      "290\n",
      "[80073, 44536] [[0, 0], [1, 1], [2, 2]] 2\n",
      "300\n",
      "[87841, 43920] [[0, 0], [1, 2], [2, 2]] 2\n",
      "[64801, 102480] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[10081, 175680] [[0, 0], [1, 1], [2, 2]] 2\n",
      "310\n",
      "[97293, 16276] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[93433, 53256] [[0, 0], [1, 1], [2, 2]] 2\n",
      "320\n",
      "[104181, 24700] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[29449, 179400] [[0, 0], [1, 1], [2, 2]] 2\n",
      "330\n",
      "[43289, 173160] [[0, 0], [2, 1], [2, 2]] 2\n",
      "[63393, 150976] [[0, 0], [1, 1], [2, 2]] 2\n",
      "340\n",
      "[68901, 160540] [[0, 0], [1, 1], [2, 2]] 2\n",
      "350\n",
      "[30973, 216036] [[0, 0], [1, 1], [2, 2]] 2\n",
      "360\n",
      "[132441, 20440] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[126169, 61320] [[0, 0], [1, 1], [2, 2]] 2\n",
      "370\n",
      "[16629, 261100] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[116529, 120640] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[108273, 138736] [[0, 0], [1, 1], [2, 2]] 2\n",
      "380\n",
      "[94677, 185164] [[0, 0], [1, 1], [2, 2]] 2\n",
      "390\n",
      "[67609, 238200] [[0, 0], [1, 1], [2, 2]] 2\n",
      "400\n",
      "[159037, 33684] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[148237, 112884] [[0, 0], [1, 1], [2, 2]] 2\n",
      "410\n",
      "420\n",
      "[176341, 25260] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[171409, 81600] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[5901, 355300] [[0, 0], [1, 1], [2, 2]] 2\n",
      "430\n",
      "[158589, 147220] [[0, 0], [1, 1], [2, 2]] 2\n",
      "440\n",
      "[881, 388080] [[0, 0], [2, 1], [2, 2]] 2\n",
      "[189561, 81880] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[134521, 224280] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[58717, 339444] [[0, 0], [1, 1], [2, 2]] 2\n",
      "450\n",
      "[168849, 182800] [[0, 0], [1, 1], [2, 2]] 2\n",
      "460\n",
      "[95557, 315324] [[0, 0], [1, 1], [2, 2]] 2\n",
      "470\n",
      "480\n",
      "[230337, 30784] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[37761, 423280] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[233109, 44620] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[224821, 98940] [[0, 0], [1, 1], [2, 2]] 2\n",
      "490\n",
      "[220549, 147900] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[210649, 177480] [[0, 0], [1, 1], [2, 2]] 2\n",
      "500\n",
      "[184269, 268660] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[39729, 468640] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[186181, 274860] [[0, 0], [1, 1], [2, 2]] 2\n",
      "510\n",
      "520\n",
      "[141841, 375120] [[0, 0], [1, 1], [2, 2]] 2\n",
      "530\n",
      "[274089, 106600] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[119253, 432796] [[0, 0], [1, 1], [2, 2]] 2\n",
      "540\n",
      "[79237, 499884] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[295869, 37060] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[250369, 235440] [[0, 0], [1, 1], [2, 2]] 2\n",
      "550\n",
      "[274149, 211660] [[0, 0], [1, 1], [2, 2]] 2\n",
      "560\n",
      "[198121, 393240] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[7861, 630540] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[245361, 318640] [[0, 0], [1, 1], [2, 2]] 2\n",
      "570\n",
      "[330429, 57700] [[0, 0], [1, 1], [2, 2]] 2\n",
      "580\n",
      "590\n",
      "[105633, 588256] [[0, 0], [1, 1], [2, 2]] 2\n",
      "600\n",
      "[277101, 348580] [[0, 0], [1, 1], [2, 2]] 2\n",
      "610\n",
      "[374473, 44136] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[367693, 140676] [[0, 0], [1, 1], [2, 2]] 2\n",
      "620\n",
      "[202269, 542500] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[383977, 135864] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[38037, 752284] [[0, 0], [1, 1], [2, 2]] 2\n",
      "630\n",
      "640\n",
      "[357057, 297424] [[0, 0], [1, 1], [2, 2]] 2\n",
      "650\n",
      "[269593, 517176] [[0, 0], [1, 1], [2, 2]] 2\n",
      "660\n",
      "[298537, 491784] [[0, 0], [1, 1], [2, 2]] 2\n",
      "670\n",
      "[196893, 681076] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[455413, 73116] [[0, 0], [1, 1], [2, 2]] 2\n",
      "680\n",
      "[467781, 52060] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[438949, 238380] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[460321, 165360] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[195937, 727584] [[0, 0], [1, 1], [2, 2]] 2\n",
      "690\n",
      "[441709, 292740] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[96433, 869856] [[0, 0], [1, 1], [2, 2]] 2\n",
      "700\n",
      "[395301, 434620] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[407817, 436744] [[0, 0], [1, 1], [2, 2]] 2\n",
      "710\n",
      "720\n",
      "[354229, 600300] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[312181, 669900] [[0, 0], [1, 1], [2, 2]] 2\n",
      "730\n",
      "[523833, 170056] [[0, 0], [1, 1], [2, 2]] 2\n",
      "740\n",
      "[493521, 369520] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[276241, 786720] [[0, 0], [1, 1], [2, 2]] 2\n",
      "750\n",
      "[176149, 953820] [[0, 0], [1, 1], [2, 2]] 2\n",
      "760\n",
      "[577521, 60880] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[168861, 999700] [[0, 0], [1, 1], [2, 2]] 2\n",
      "770\n",
      "[549129, 340120] [[0, 0], [1, 1], [2, 2]] 2\n",
      "780\n",
      "[612861, 91060] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[512541, 505540] [[0, 0], [1, 1], [2, 2]] 2\n",
      "790\n",
      "[594253, 294996] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[315249, 888160] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[26809, 1243320] [[0, 0], [1, 1], [2, 2]] 2\n",
      "800\n",
      "[545581, 533940] [[0, 0], [1, 1], [2, 2]] 2\n",
      "810\n",
      "820\n",
      "[371541, 903100] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[139641, 1226920] [[0, 0], [1, 1], [2, 2]] 2\n",
      "830\n",
      "840\n",
      "[705517, 70644] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[698649, 209560] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[696601, 223080] [[0, 0], [1, 1], [2, 2]] 2\n",
      "850\n",
      "[674709, 392380] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[664753, 452496] [[0, 0], [1, 1], [2, 2]] 2\n",
      "860\n",
      "[635329, 581280] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[304669, 1152180] [[0, 0], [1, 1], [2, 2]] 2\n",
      "870\n",
      "[592729, 736680] [[0, 0], [1, 1], [2, 2]] 2\n",
      "880\n",
      "[573661, 792900] [[0, 0], [1, 1], [2, 2]] 2\n",
      "890\n",
      "900\n",
      "[807957, 111724] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[484617, 1030744] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[468561, 1071520] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[82861, 1552980] [[0, 0], [1, 1], [2, 2]] 2\n",
      "910\n",
      "920\n",
      "[853689, 81400] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[362821, 1298700] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[843997, 256404] [[0, 0], [1, 1], [2, 2]] 2\n",
      "930\n",
      "[820369, 449760] [[0, 0], [1, 1], [2, 2]] 2\n",
      "940\n",
      "[277081, 1467960] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[778101, 664300] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[632277, 983164] [[0, 0], [1, 1], [2, 2]] 2\n",
      "950\n",
      "[202609, 1601040] [[0, 0], [1, 1], [2, 2]] 2\n",
      "960\n",
      "[913801, 254760] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[712201, 903240] [[0, 0], [1, 1], [2, 2]] 2\n",
      "970\n",
      "[876129, 547120] [[0, 0], [1, 1], [2, 2]] 2\n",
      "980\n",
      "[617389, 1170180] [[0, 0], [1, 1], [2, 2]] 2\n",
      "[1969, 1938480] [[0, 0], [1, 1], [2, 2]] 2\n",
      "990\n",
      "[796873, 885336] [[0, 0], [1, 1], [2, 2]] 2\n",
      "1000\n",
      "[[0, 0], [9, 40], [133, 156], [273, 136], [189, 340], [33, 544], [399, 40], [561, 400], [57, 1624], [399, 1600], [1173, 1036], [1581, 820], [89, 3960], [1513, 3816], [3577, 1464], [3901, 2340], [2461, 5460], [973, 9636], [7029, 2380], [5289, 7480], [5617, 8544], [1309, 17460], [9717, 4444], [5797, 17004], [12513, 3616], [12921, 13000], [4369, 32880], [20701, 5220], [20349, 7540], [18601, 17880], [12549, 34540], [337, 56784], [2359, 56760], [26329, 20760], [32361, 7240], [29869, 24420], [15729, 50320], [22849, 46320], [37909, 11820], [31621, 41820], [8901, 74620], [48357, 9724], [12741, 83980], [47817, 31144], [37389, 60580], [58065, 1928], [34977, 73264], [64893, 17476], [69649, 12720], [57229, 60420], [66277, 41964], [57129, 77560], [34861, 118020], [39421, 121380], [80073, 44536], [87841, 43920], [64801, 102480], [10081, 175680], [97293, 16276], [93433, 53256], [104181, 24700], [29449, 179400], [43289, 173160], [63393, 150976], [68901, 160540], [30973, 216036], [132441, 20440], [126169, 61320], [16629, 261100], [116529, 120640], [108273, 138736], [94677, 185164], [67609, 238200], [159037, 33684], [148237, 112884], [176341, 25260], [171409, 81600], [5901, 355300], [158589, 147220], [881, 388080], [189561, 81880], [134521, 224280], [58717, 339444], [168849, 182800], [95557, 315324], [230337, 30784], [37761, 423280], [233109, 44620], [224821, 98940], [220549, 147900], [210649, 177480], [184269, 268660], [39729, 468640], [186181, 274860], [141841, 375120], [274089, 106600], [119253, 432796], [79237, 499884], [295869, 37060], [250369, 235440], [274149, 211660], [198121, 393240], [7861, 630540], [245361, 318640], [330429, 57700], [105633, 588256], [277101, 348580], [374473, 44136], [367693, 140676], [202269, 542500], [383977, 135864], [38037, 752284], [357057, 297424], [269593, 517176], [298537, 491784], [196893, 681076], [455413, 73116], [467781, 52060], [438949, 238380], [460321, 165360], [195937, 727584], [441709, 292740], [96433, 869856], [395301, 434620], [407817, 436744], [354229, 600300], [312181, 669900], [523833, 170056], [493521, 369520], [276241, 786720], [176149, 953820], [577521, 60880], [168861, 999700], [549129, 340120], [612861, 91060], [512541, 505540], [594253, 294996], [315249, 888160], [26809, 1243320], [545581, 533940], [371541, 903100], [139641, 1226920], [705517, 70644], [698649, 209560], [696601, 223080], [674709, 392380], [664753, 452496], [635329, 581280], [304669, 1152180], [592729, 736680], [573661, 792900], [807957, 111724], [484617, 1030744], [468561, 1071520], [82861, 1552980], [853689, 81400], [362821, 1298700], [843997, 256404], [820369, 449760], [277081, 1467960], [778101, 664300], [632277, 983164], [202609, 1601040], [913801, 254760], [712201, 903240], [876129, 547120], [617389, 1170180], [1969, 1938480], [796873, 885336]]\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "\n",
    "n=20\n",
    "N=1000\n",
    "A_B=[[0,0]]\n",
    "A=3\n",
    "B=4\n",
    "cnt2=0\n",
    "\n",
    "for s in range(1,N+1):\n",
    "    if(s%10==0):\n",
    "        print(s)\n",
    "    for t in range (1,s+1):\n",
    "        if (((s+t)%2)==0):\n",
    "            continue\n",
    "        if (math.gcd(s,t))!=1:\n",
    "            continue\n",
    "        A=s**2-t**2\n",
    "        B=2*s*t\n",
    "\n",
    "        a_b=[[0,0]]\n",
    "        cnt=0\n",
    "        for i in range(1,n+1):\n",
    "            for j in range (1,n+1):\n",
    "                Ap=A**i\n",
    "                Bp=B**j\n",
    "                ApBp=Ap+Bp\n",
    "                sqApBp=math.sqrt(ApBp)\n",
    "                Rootc=math.ceil(sqApBp)\n",
    "                Rootf=math.floor(sqApBp)\n",
    "                if (ApBp==Rootc**2) or (ApBp==Rootf**2):\n",
    "                    a_b.append([i,j])\n",
    "                cnt+=1\n",
    "\n",
    "        if(len(a_b)!=2):\n",
    "            cnt2+=1\n",
    "            A_B.append([A,B])\n",
    "            print(A_B[cnt2],a_b,len(a_b)-1)\n",
    "print(A_B)"
   ]
  }
 ],
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