<video><caption><image_15>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt with white stripes and appears to be in a classroom or a similar setting. The man is pointing to something written on the chalkboard with his right hand. The text on the board reads "Quil o resto no divisio de 2" which translates to "What is the difference between 2 and 3?" in Portuguese. There is also a logo on the right side of the image.</caption><caption><image_16>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt with white stripes and appears to be in a classroom or classroom setting. The man is pointing upwards with his right hand and has a serious expression on his face. On the chalkboard, there is a question written in white chalk that reads "Qui o roblo no diviso de 2" which translates to "How to solve a problem with 2". There is also a logo of the European Union on the right side of the image.</caption></video><transcript><audio_17> 7 por 11 por 19 e confira se isso de fato dá 1.463. Bom, feito isso, percebido isso, eu quero te propor o seguinte. Vamos encontrar...</transcript><caption><image_18>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt and appears to be in a classroom or a classroom setting. The man is pointing towards the chalkboard with his right hand and is gesturing with his left hand. On the chalk board, there is a question written in Portuguese that reads "Quil o resto no divisão do 2 for 1460? L2.1.9". The question is written in white chalk and is accompanied by a small logo on the right side of the board.</caption><transcript><audio_19> desse número, 2 elevado a 327, primeiramente módulo 7, depois módulo 11 e depois módulo 19. Fazer isso vai ser aplicável.</transcript><transcript><audio_20> Vamos primeiramente encontrar a classe de equivalência de 2 elevado a 327, módulo 7. O fato desse número ser primo me</transcript><video><caption><image_21>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt with white stripes and appears to be in a classroom or classroom setting. On the chalkboard, there is a question written in Portuguese that reads "Quil o resto no divisão de 2? for 1463? L. 3-11-19". The man is looking directly at the camera with a serious expression on his face.</caption><caption><image_22>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt with white stripes on the sleeves. He has short dark hair and is smiling at the camera. On the chalkboard, there are two equations written in white chalk. The equations are written in Portuguese and appear to be related to mathematics. The man is pointing to one of the equations with his right hand.</caption></video><caption><image_23>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt and appears to be writing on the chalkboard with his right hand. The text on the board is written in white chalk and is in Portuguese. The man is pointing to the right side of the board with his left hand, as if he is explaining something. The background is blurred, but it seems like the man is in a classroom or a classroom setting.</caption><transcript><audio_24> Portanto, eu vou pegar o 327 e vou dividir por P menos 1.</transcript><transcript><audio_25> Depois desce o 7. 4 vezes 6 dá 24.</transcript><transcript><audio_26> reescrever esse número da seguinte forma, 2 elevado a 6, que por sua vez está elevado a 54,</transcript><video><caption><image_27>The image shows a man standing in front of a green blackboard. He is wearing a black t-shirt and appears to be a teacher or a student. On the blackboard, there are two equations written in white chalk. The equations are written in Portuguese and appear to be related to mathematics. The man is looking up at the equations with a serious expression on his face.</caption><caption><image_28>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt and appears to be writing on the chalkboard with a marker. The text on the board reads "Quil o resto no divo" which translates to "What is the difference between two numbers?" in English. Below the text, there is a question written in Portuguese. The question is asking the viewer if they are trying to solve a mathematical problem.</caption></video> this pause the video and multiply 7 by 11 by 19 and check if this actually gives 1463 well done that understood that and I want to propose the following let's find the equivalence class  of this number 2 raised to 327 first modulo 7 then here is mulo 19 doing this will be the first step of our solution let's first find the equivalence class of 2 elev 327 modulo 7 The fact that this number is prime allows me to use the little FM theorem so I'm going to take 327 and I'm going to divide it by p- 1 which is 6 this will give 6 x 5 30 4 x 6 gives 24 and the remainder is 3 this then allows me to rewrite this number as 2 raised 6 which in turn is raised to
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