{"segments": [{"id": 1, "seek": 2656, "start": 0.76, "end": 26.56, "text": "بسم الله الرحمن الرحيم هذه هي المحاضرة الثامنة مساق رياضيات منفصلة طلاب و طالبات الجامعة الإسلامية قسم الحوسبة المتنقلة كلية العلو و كلية تكنولوجيا المعلومات المحاضرة اليوم ان شاء الله هنحكي عن اللي هو section 4.4 اللي هو solving congruences او حل التطابقات", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 39896, 9673, 5016, 46958, 25720, 6024, 104, 10943, 1863, 3660, 47524, 995, 4587, 12602, 1829, 46958, 1829, 9307, 9154, 5172, 36520, 3660, 23032, 15040, 3555, 4032, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 21542, 2407, 35457, 3660, 9673, 2655, 1863, 4587, 37977, 28242, 10632, 18863, 1211, 2407, 4032, 28242, 10632, 6055, 19452, 12610, 29245, 25528, 9673, 30241, 20498, 9307, 9673, 5016, 46958, 25720, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 5016, 4117, 1829, 18871, 13672, 1829, 31439, 3541, 1017, 13, 19, 13672, 1829, 31439, 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"temperature": 1.0}, {"id": 17, "seek": 35749, "start": 342.73, "end": 357.49, "text": "الـ12 والنقص 2 والـ19 وكل هنا دولة برضه بيكون ال inverse للتلاتة modulo 7 لإن اللي هنا كلهم بطابق من الخمسة اللي لجيناها modulo 7", "tokens": [6027, 39184, 4762, 16070, 1863, 4587, 9381, 568, 16070, 39184, 3405, 4032, 28820, 34105, 11778, 12610, 3660, 4724, 43042, 3224, 4724, 1829, 30544, 2423, 17340, 24976, 2655, 1211, 9307, 3660, 1072, 13455, 1614, 5296, 28814, 1863, 13672, 1829, 8032, 8315, 28242, 16095, 4724, 9566, 16758, 4587, 9154, 33962, 2304, 3794, 3660, 13672, 1829, 5296, 7435, 1829, 8315, 11296, 1072, 13455, 1614], "avg_logprob": -0.30090725854519873, "compression_ratio": 1.4444444444444444, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 342.73, "end": 343.45, "word": "الـ12", "probability": 0.50537109375}, {"start": 343.45, "end": 344.43, "word": " والنقص", "probability": 0.7020263671875}, {"start": 344.43, "end": 344.91, "word": " 2", "probability": 0.82275390625}, 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352.69, "end": 353.11, "word": " اللي", "probability": 0.71923828125}, {"start": 353.11, "end": 353.49, "word": " هنا", "probability": 0.4385986328125}, {"start": 353.49, "end": 353.97, "word": " كلهم", "probability": 0.91455078125}, {"start": 353.97, "end": 354.53, "word": " بطابق", "probability": 0.9295654296875}, {"start": 354.53, "end": 354.67, "word": " من", "probability": 0.156982421875}, {"start": 354.67, "end": 355.39, "word": " الخمسة", "probability": 0.9405517578125}, {"start": 355.39, "end": 355.63, "word": " اللي", "probability": 0.971923828125}, {"start": 355.63, "end": 356.23, "word": " لجيناها", "probability": 0.71650390625}, {"start": 356.23, "end": 356.79, "word": " modulo", "probability": 0.93994140625}, {"start": 356.79, "end": 357.49, "word": " 7", "probability": 0.93603515625}], "temperature": 1.0}, {"id": 18, "seek": 38412, "start": 363.84, "end": 384.12, "text": "طيب شوف خلونا نجد كيف نجد ال inverse اللي هو للعدد لأي عدد بدنيا بالنسبة لقياس معين ال Euclidean algorithm اللي هي خورزمية القسمة و بذوذ coefficients اللي هو بتعطينا gives us a systematic approach to find اللي هو إيش to find inverse كيف؟", "tokens": [9566, 1829, 3555, 13412, 38688, 16490, 1211, 2407, 8315, 8717, 7435, 3215, 9122, 33911, 8717, 7435, 3215, 2423, 17340, 13672, 1829, 31439, 5296, 1211, 22488, 3215, 5296, 10721, 1829, 6225, 3215, 3215, 47525, 22653, 995, 20666, 1863, 35457, 3660, 5296, 4587, 25528, 3794, 20449, 9957, 2423, 462, 1311, 31264, 282, 9284, 13672, 1829, 39896, 16490, 13063, 11622, 2304, 10632, 25062, 38251, 3660, 4032, 4724, 8848, 2407, 8848, 31994, 13672, 1829, 31439, 39894, 3615, 9566, 1829, 8315, 2709, 505, 257, 27249, 3109, 281, 915, 13672, 1829, 31439, 11933, 1829, 8592, 281, 915, 17340, 9122, 33911, 22807], "avg_logprob": -0.3038737007106344, "compression_ratio": 1.5580357142857142, "no_speech_prob": 0.0, "words": [{"start": 363.84, "end": 364.14, "word": "طيب", "probability": 0.5902913411458334}, {"start": 364.14, "end": 364.4, "word": " شوف", 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0.4732666015625}, {"start": 375.76, "end": 376.26, "word": " coefficients", "probability": 0.8583984375}, {"start": 376.26, "end": 377.2, "word": " اللي", "probability": 0.967041015625}, {"start": 377.2, "end": 377.44, "word": " هو", "probability": 0.50439453125}, {"start": 377.44, "end": 378.2, "word": " بتعطينا", "probability": 0.8986328125}, {"start": 378.2, "end": 378.42, "word": " gives", "probability": 0.378662109375}, {"start": 378.42, "end": 378.74, "word": " us", "probability": 0.7060546875}, {"start": 378.74, "end": 378.94, "word": " a", "probability": 0.9560546875}, {"start": 378.94, "end": 379.4, "word": " systematic", "probability": 0.81005859375}, {"start": 379.4, "end": 379.98, "word": " approach", "probability": 0.9501953125}, {"start": 379.98, "end": 380.2, "word": " to", "probability": 0.8720703125}, {"start": 380.2, "end": 380.62, "word": " find", "probability": 0.9111328125}, {"start": 380.62, "end": 380.94, "word": " اللي", "probability": 0.72021484375}, {"start": 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"start": 567.2, "end": 588.6, "text": "وبنه بتجيب اللي هو الـ grades common divisor as a linear combination of الاتنين وبكون المعامل الـ 101 هو ال inverse المطلوب خلّينا نشوف الكلام هذا عمليًا الان اولًا استخدم ال algorithm to show that ال grades common divisor بين هدول العددين بساوة واحد ايش بنسوي؟ بنقسم هذا على هذا جسمنا على 101", "tokens": [37746, 1863, 3224, 39894, 7435, 1829, 3555, 13672, 1829, 31439, 2423, 39184, 18041, 2689, 25974, 284, 382, 257, 8213, 6562, 295, 2423, 9307, 1863, 9957, 4032, 3555, 30544, 9673, 3615, 10943, 1211, 2423, 39184, 21055, 31439, 2423, 17340, 9673, 9566, 1211, 37746, 16490, 1211, 11703, 9957, 995, 8717, 8592, 38688, 2423, 28820, 10943, 23758, 6225, 2304, 20292, 14111, 995, 2423, 7649, 1975, 12610, 14111, 995, 1975, 14851, 9778, 40448, 2423, 9284, 281, 855, 300, 2423, 18041, 2689, 25974, 284, 49374, 8032, 3215, 12610, 18863, 3215, 3215, 9957, 4724, 3794, 995, 2407, 3660, 36764, 24401, 1975, 1829, 8592, 44945, 3794, 45865, 22807, 44945, 4587, 38251, 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الآن ان شاء الله و بعد شوية نشوف ال chinese remandatory يعني", "tokens": [6027, 20292, 31439, 8717, 12984, 3555, 2655, 29538, 41950, 16572, 28671, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 6024, 48506, 16472, 13412, 16606, 21984, 4032, 39182, 13412, 2407, 10632, 8717, 8592, 38688, 2423, 47272, 890, 474, 4745, 37495, 22653], "avg_logprob": -0.3269531227648258, "compression_ratio": 1.2598425196850394, "no_speech_prob": 0.0, "words": [{"start": 1030.23, "end": 1030.57, "word": "اللي", "probability": 0.37322998046875}, {"start": 1030.57, "end": 1030.75, "word": " هو", "probability": 0.73681640625}, {"start": 1030.75, "end": 1031.29, "word": " نثبت", "probability": 0.854248046875}, {"start": 1031.29, "end": 1031.47, "word": " هذه", "probability": 0.76123046875}, {"start": 1031.47, "end": 1031.91, "word": " الطريقة", "probability": 0.9895833333333334}, {"start": 1031.91, "end": 1032.05, "word": " اللي", "probability": 0.878173828125}, {"start": 1032.05, "end": 1032.83, "word": " أخدناها", 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remainder theorem اللي الآن احنا هندرس ايه اللي هو كيف اللي هي ايش النظرية بتقول متى بيكون حل و كيف بنحل اللي هو التطابقات", "tokens": [2407, 29538, 13672, 1829, 39896, 13672, 1829, 4724, 1829, 5016, 1211, 11296, 6225, 18513, 3660, 24525, 2304, 11296, 2423, 47272, 29837, 20904, 13672, 1829, 6024, 48506, 1975, 5016, 8315, 8032, 41260, 2288, 3794, 1975, 1829, 3224, 13672, 1829, 31439, 9122, 33911, 13672, 1829, 39896, 1975, 1829, 8592, 28239, 19913, 2288, 10632, 39894, 39648, 44650, 7578, 4724, 1829, 30544, 11331, 1211, 4032, 9122, 33911, 44945, 5016, 1211, 13672, 1829, 31439, 16712, 9566, 16758, 4587, 9307], "avg_logprob": -0.19572916348775227, "compression_ratio": 1.6904761904761905, "no_speech_prob": 0.0, "words": [{"start": 1209.04, "end": 1209.32, "word": "و", "probability": 0.74462890625}, {"start": 1209.32, "end": 1209.78, "word": " هذه", "probability": 0.459716796875}, {"start": 1209.78, "end": 1210.1, "word": " اللي", "probability": 0.662109375}, {"start": 1210.1, "end": 1210.42, 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بالشكل هذا و كلهم المجهول فيهم X و ال M1 و ال M2 و ال MN كلهم relatively prime بتقولك ال Chinese remainder theorem إذا يوجد حل مشترك وحيد لهذه المجموعات اللي هو has a unique solution modulo M اللي هو M", "tokens": [1211, 2407, 25961, 8978, 18871, 16254, 1185, 295, 8213, 8882, 84, 2667, 20666, 8592, 28820, 23758, 4032, 28242, 16095, 9673, 7435, 3224, 12610, 8978, 16095, 1783, 4032, 2423, 376, 16, 4032, 2423, 376, 17, 4032, 2423, 376, 45, 28242, 16095, 7226, 5835, 39894, 39648, 4117, 2423, 4649, 29837, 20904, 11933, 15730, 7251, 29245, 3215, 11331, 1211, 37893, 2655, 31747, 4032, 5016, 25708, 46740, 24192, 9673, 7435, 2304, 45367, 9307, 13672, 1829, 31439, 575, 257, 3845, 3827, 1072, 13455, 376, 13672, 1829, 31439, 376], "avg_logprob": -0.30208333404291243, "compression_ratio": 1.4870689655172413, "no_speech_prob": 0.0, "words": [{"start": 1262.91, "end": 1263.31, "word": "لو", "probability": 0.79296875}, {"start": 1263.31, "end": 1263.51, "word": " كان", "probability": 0.95849609375}, 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0.36962890625}], "temperature": 1.0}, {"id": 60, "seek": 130209, "start": 1285.42, "end": 1302.1, "text": "م1 م2 في مين في من يعني بتقولك الآن اللي هي chinese remainder theorem لو كان عندك فيه system من اللي هو ال linear congruences هذه تطابق اي واحد مدل ام واحد وال X تطابق اتنين مدل ام اتنين", "tokens": [2304, 16, 3714, 17, 8978, 3714, 9957, 8978, 3714, 1863, 37495, 22653, 39894, 39648, 4117, 6024, 48506, 13672, 1829, 39896, 47272, 29837, 20904, 45164, 25961, 43242, 4117, 8978, 3224, 1185, 9154, 13672, 1829, 31439, 2423, 8213, 8882, 84, 2667, 29538, 6055, 9566, 16758, 4587, 1975, 1829, 36764, 24401, 3714, 3215, 1211, 1975, 2304, 36764, 24401, 16070, 1783, 6055, 9566, 16758, 4587, 1975, 2655, 1863, 9957, 3714, 3215, 1211, 1975, 2304, 1975, 2655, 1863, 9957], "avg_logprob": -0.29812499046325686, "compression_ratio": 1.5921787709497206, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1285.42, "end": 1286.08, "word": "م1", "probability": 0.5572509765625}, {"start": 1286.08, "end": 1286.78, "word": " م2", "probability": 0.6966552734375}, {"start": 1286.78, "end": 1287.04, "word": " في", "probability": 0.346923828125}, {"start": 1287.04, "end": 1287.42, "word": " مين", "probability": 0.85791015625}, {"start": 1287.42, "end": 1287.64, "word": " في", "probability": 0.65869140625}, {"start": 1287.64, "end": 1288.3, "word": " من", "probability": 0.4781494140625}, {"start": 1288.3, "end": 1289.04, "word": " يعني", "probability": 0.6505126953125}, {"start": 1289.04, "end": 1289.66, "word": " بتقولك", "probability": 0.7687174479166666}, {"start": 1289.66, "end": 1290.2, "word": " الآن", "probability": 0.6468505859375}, {"start": 1290.2, "end": 1290.52, "word": " اللي", "probability": 0.90966796875}, {"start": 1290.52, "end": 1290.62, "word": " هي", "probability": 0.64453125}, {"start": 1290.62, "end": 1291.08, "word": " chinese", "probability": 0.5107421875}, {"start": 1291.08, "end": 1291.54, "word": " remainder", "probability": 0.669921875}, {"start": 1291.54, "end": 1291.92, "word": " theorem", "probability": 0.7861328125}, {"start": 1291.92, "end": 1292.14, "word": " لو", "probability": 0.77783203125}, {"start": 1292.14, "end": 1292.4, "word": " كان", "probability": 0.98828125}, {"start": 1292.4, "end": 1292.82, "word": " عندك", "probability": 0.991943359375}, {"start": 1292.82, "end": 1293.18, "word": " فيه", "probability": 0.81005859375}, {"start": 1293.18, "end": 1293.92, "word": " system", "probability": 0.88427734375}, {"start": 1293.92, "end": 1294.96, "word": " من", "probability": 0.962890625}, {"start": 1294.96, "end": 1295.46, "word": " اللي", "probability": 0.9814453125}, {"start": 1295.46, "end": 1295.8, "word": " هو", "probability": 0.97216796875}, {"start": 1295.8, "end": 1296.12, "word": " ال", "probability": 0.931640625}, {"start": 1296.12, "end": 1296.58, "word": " linear", "probability": 0.81103515625}, {"start": 1296.58, "end": 1297.62, "word": " congruences", "probability": 0.6666666666666666}, {"start": 1297.62, "end": 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