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+{"segments": [{"id": 1, "seek": 4397, "start": 19.35, "end": 43.97, "text": "بسم الله الرحمن الرحيم المحاضرة اليوم محاضرة رقم عشرين في مساق نظرية الأعداد لطلبة الجامعة الإسلامية قسم رياضيات كليتي التربية والعلوم هنكمل في chapter 6 اللي بدناه اللي بتحدث عن number theoretic functions", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 5016, 46958, 25720, 45595, 20498, 3714, 5016, 46958, 25720, 12602, 4587, 2304, 6225, 46309, 9957, 8978, 47524, 995, 4587, 8717, 19913, 2288, 10632, 16247, 22488, 18513, 5296, 9566, 46152, 3660, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 12602, 1829, 46958, 1829, 9307, 9122, 20292, 31371, 16712, 25513, 10632, 16070, 30241, 20498, 8032, 1863, 24793, 1211, 8978, 7187, 1386, 13672, 1829, 47525, 8315, 3224, 13672, 1829, 39894, 24401, 12984, 18871, 1230, 14308, 299, 6828], "avg_logprob": -0.0874818294027517, "compression_ratio": 1.6796116504854368, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 19.35, 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0.9208984375}, {"start": 127.92, "end": 128.76, "word": " بلزمنا", "probability": 0.83583984375}, {"start": 128.76, "end": 129.28, "word": " ندرس", "probability": 0.9947509765625}, {"start": 129.28, "end": 130.0, "word": " خواص", "probability": 0.7955729166666666}, {"start": 130.0, "end": 131.2, "word": " إضافية", "probability": 0.8907470703125}], "temperature": 1.0}, {"id": 6, "seek": 15666, "start": 131.79, "end": 156.67, "text": "الـ Sigma والـ Tau اللي من خلالها ان شاء الله هنقدر نحصل على طريقة سهلة أو طرق سهلة لإيجاد sum of divisors و number of divisors و أيضا لدراسة خلاص sum of divisors و number of divisors حكينا المرة الماضية برضه نظرية ستة واحد قلنا", "tokens": [6027, 39184, 36595, 16070, 39184, 314, 1459, 13672, 1829, 9154, 16490, 1211, 6027, 11296, 16472, 13412, 16606, 21984, 8032, 1863, 28543, 2288, 8717, 5016, 36520, 15844, 23032, 16572, 28671, 8608, 3224, 37977, 34051, 23032, 2288, 4587, 8608, 3224, 37977, 5296, 28814, 1829, 7435, 18513, 2408, 295, 25974, 830, 4032, 1230, 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"probability": 0.898681640625}, {"start": 156.23, "end": 156.67, "word": " قلنا", "probability": 0.88037109375}], "temperature": 1.0}, {"id": 7, "seek": 17345, "start": 157.71, "end": 173.45, "text": "لو كان عندي N أي عدد أكبر من عدد أكبر من واحد أي عدد أكبر من واحد N أكيد الـ N الأكبر من واحد في الـ unique factorization theorem بنقدر نكتبه على صورة اللي هو bar of the brines اللي هي B1", "tokens": [1211, 2407, 25961, 18871, 16254, 426, 36632, 6225, 3215, 3215, 5551, 4117, 26890, 9154, 6225, 3215, 3215, 5551, 4117, 26890, 9154, 36764, 24401, 36632, 6225, 3215, 3215, 5551, 4117, 26890, 9154, 36764, 24401, 426, 5551, 4117, 25708, 2423, 39184, 426, 16247, 4117, 26890, 9154, 36764, 24401, 8978, 2423, 39184, 3845, 5952, 2144, 20904, 44945, 28543, 2288, 8717, 4117, 2655, 3555, 3224, 15844, 20328, 13063, 3660, 13672, 1829, 31439, 2159, 295, 264, 738, 1652, 13672, 1829, 39896, 363, 16], "avg_logprob": -0.2189477814149253, "compression_ratio": 1.6551724137931034, "no_speech_prob": 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واحد زائد واحد ناقص واحد على بي واحد ناقص R كله هنا بنفس الأسلوب لعن بي R كي R زائد واحد ناقص واحد على بي R ناقص واحد خلينا للرسول للبرهان بخلينا بس نطلعنا على مثال هيك على جنب و نشوف كيف بدنا نروح باتجاه البرهان", "tokens": [2304, 33599, 1829, 21542, 6027, 11331, 33546, 1211, 48812, 25513, 34105, 4724, 1829, 30544, 13672, 1829, 31439, 1230, 295, 25974, 830, 2423, 7649, 2408, 295, 25974, 830, 31439, 6225, 3555, 9640, 3660, 18871, 4724, 1829, 36764, 24401, 9122, 1829, 36764, 24401, 5551, 3794, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 15844, 4724, 1829, 36764, 24401, 8717, 995, 4587, 9381, 497, 28242, 3224, 34105, 44945, 36178, 16247, 3794, 1211, 37746, 5296, 3615, 1863, 4724, 1829, 497, 9122, 1829, 497, 30767, 16373, 3215, 36764, 24401, 8717, 995, 4587, 9381, 36764, 24401, 15844, 4724, 1829, 497, 8717, 995, 4587, 9381, 36764, 24401, 16490, 1211, 9957, 995, 24976, 2288, 3794, 12610, 24976, 26890, 3224, 7649, 4724, 9778, 1211, 9957, 995, 4724, 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{"start": 296.24, "end": 296.72, "word": " واحد", "probability": 0.986572265625}, {"start": 296.72, "end": 297.32, "word": " على", "probability": 0.7666015625}, {"start": 297.32, "end": 297.6, "word": " بي", "probability": 0.984375}, {"start": 297.6, "end": 297.92, "word": " R", "probability": 0.5654296875}, {"start": 297.92, "end": 298.5, "word": " ناقص", "probability": 0.99658203125}, {"start": 298.5, "end": 299.02, "word": " واحد", "probability": 0.986328125}, {"start": 299.02, "end": 299.58, "word": " خلينا", "probability": 0.7403564453125}, {"start": 299.58, "end": 300.12, "word": " للرسول", "probability": 0.77276611328125}, {"start": 300.12, "end": 300.6, "word": " للبرهان", "probability": 0.92041015625}, {"start": 300.6, "end": 301.02, "word": " بخلينا", "probability": 0.881640625}, {"start": 301.02, "end": 301.18, "word": " بس", "probability": 0.9482421875}, {"start": 301.18, "end": 301.86, "word": " نطلعنا", "probability": 0.746435546875}, {"start": 301.86, "end": 302.04, 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{"start": 316.79, "end": 317.11, "word": " عندي", "probability": 0.725830078125}, {"start": 317.11, "end": 317.37, "word": " هذا", "probability": 0.91552734375}, {"start": 317.37, "end": 317.57, "word": " بدي", "probability": 0.4520263671875}, {"start": 317.57, "end": 317.91, "word": " أشوف", "probability": 0.9422200520833334}, {"start": 317.91, "end": 318.23, "word": " له", "probability": 0.21826171875}, {"start": 318.23, "end": 319.29, "word": " الـ", "probability": 0.796875}, {"start": 319.29, "end": 319.95, "word": " divisors", "probability": 0.78564453125}, {"start": 319.95, "end": 321.01, "word": " تبعونه", "probability": 0.925}, {"start": 321.01, "end": 322.47, "word": " اتفجنا", "probability": 0.90068359375}, {"start": 322.47, "end": 323.37, "word": " أن", "probability": 0.462646484375}, {"start": 323.37, "end": 323.63, "word": " الـ", "probability": 0.764892578125}, {"start": 323.63, "end": 324.33, "word": " divisors", "probability": 0.937255859375}, {"start": 324.33, "end": 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تلاتة ماشي الحال هاي شكل ال divisors اللي عندي بناء على هذه المعلومة على شكل ال divisors خليني اجي اطلع على اتنين تربيع", "tokens": [10721, 3794, 27188, 995, 1975, 2655, 1863, 9957, 11331, 1829, 12984, 27188, 995, 36764, 24401, 5551, 4117, 26890, 34051, 8608, 2407, 7578, 8608, 5172, 2288, 4032, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 10874, 16254, 8592, 1975, 2655, 1863, 9957, 4032, 27188, 995, 1975, 2655, 1863, 9957, 8032, 2655, 30544, 5551, 4117, 26890, 34051, 8608, 2407, 7578, 8608, 5172, 2288, 4032, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 3714, 9957, 6055, 1211, 9307, 3660, 3714, 33599, 1829, 21542, 6027, 8032, 47302, 13412, 28820, 2423, 25974, 830, 13672, 1829, 18871, 16254, 44945, 16606, 15844, 29538, 9673, 30241, 20498, 3660, 15844, 13412, 28820, 2423, 25974, 830, 16490, 1211, 9957, 1829, 1975, 7435, 1829, 1975, 9566, 1211, 3615, 15844, 1975, 2655, 1863, 9957, 6055, 2288, 21292, 3615], "avg_logprob": -0.22330217098626565, "compression_ratio": 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بتساوي واحد و الـ g of n بيساوي n الدالة الثابتة واحد و ال identity function g of n بيساوي n are then f and g are multiplicative أثبات سهلة لو أخدنا f", "tokens": [3555, 3615, 11242, 9673, 15040, 5016, 19913, 9307, 15844, 29910, 23275, 4724, 3615, 11242, 9673, 15040, 5016, 19913, 9307, 15844, 29910, 23275, 5551, 12610, 11331, 26108, 3660, 2423, 39184, 2445, 283, 295, 297, 39894, 3794, 995, 45865, 36764, 24401, 4032, 2423, 39184, 290, 295, 297, 4724, 1829, 3794, 995, 45865, 297, 32748, 6027, 3660, 6024, 104, 16758, 2655, 3660, 36764, 24401, 4032, 2423, 6575, 2445, 290, 295, 297, 4724, 1829, 3794, 995, 45865, 297, 366, 550, 283, 293, 290, 366, 17596, 1166, 5551, 12984, 3555, 9307, 8608, 3224, 37977, 45164, 5551, 9778, 3215, 8315, 283], "avg_logprob": -0.2403971296735108, "compression_ratio": 1.7891891891891891, "no_speech_prob": 1.8477439880371094e-06, "words": [{"start": 2270.65, "end": 2271.09, "word": "بعض", "probability": 0.9734700520833334}, {"start": 2271.09, "end": 2272.07, 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positive multiplicative ليش let and prove let اللي هو m و n element in z positive such that the greatest common divisor بين ال m و ال n بساوة واحد then", "tokens": [2670, 297, 4724, 3794, 995, 2407, 3660, 36764, 24401, 39896, 32748, 6027, 3660, 337, 633, 297, 4478, 294, 710, 3353, 17596, 1166, 32239, 8592, 718, 293, 7081, 718, 13672, 1829, 31439, 275, 4032, 297, 4478, 294, 710, 3353, 1270, 300, 264, 6636, 2689, 25974, 284, 49374, 2423, 275, 4032, 2423, 297, 4724, 3794, 995, 2407, 3660, 36764, 24401, 550], "avg_logprob": -0.27161456892887753, "compression_ratio": 1.5471698113207548, "no_speech_prob": 7.212162017822266e-06, "words": [{"start": 2298.78, "end": 2299.12, "word": "of", "probability": 0.180908203125}, {"start": 2299.12, "end": 2299.46, "word": " n", "probability": 0.5439453125}, {"start": 2299.46, "end": 2300.04, "word": " بساوة", "probability": 0.7025390625}, {"start": 2300.04, "end": 2300.58, "word": " واحد", "probability": 0.936767578125}, {"start": 2300.58, "end": 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عندك الـ F في واحد إيش هتساوي واحد واضح أه معانا يا شباب أخر نقطة قلنا Tau في عشرين لا يساوي Tau في اتنين في Tau في عشرة and", "tokens": [3555, 15042, 14739, 479, 20193, 6055, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 2423, 39184, 479, 8978, 36764, 24401, 20193, 6055, 3794, 995, 45865, 8608, 5172, 2288, 3714, 3215, 10943, 2423, 39184, 479, 8978, 36764, 24401, 20193, 6055, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 14739, 2655, 6055, 46456, 9381, 2288, 29538, 3714, 5016, 9566, 3660, 29538, 39894, 9566, 1211, 3615, 43242, 4117, 2423, 39184, 479, 8978, 36764, 24401, 11933, 1829, 8592, 8032, 2655, 3794, 995, 45865, 36764, 24401, 4032, 46958, 5016, 5551, 3224, 20449, 7649, 995, 35186, 13412, 3555, 16758, 5551, 34740, 8717, 47432, 3660, 12174, 1211, 8315, 314, 1459, 8978, 6225, 46309, 9957, 20193, 7251, 3794, 995, 45865, 314, 1459, 8978, 1975, 2655, 1863, 9957, 8978, 314, 1459, 8978, 6225, 8592, 25720, 293], "avg_logprob": -0.2702636760659516, "compression_ratio": 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