<transcript><audio_46> Resto 3. O que nos permite escrever esse número da seguinte forma, 2 elevado a 18,</transcript><video><caption><image_47>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 chalkboard is filled with mathematical equations and formulas written in white chalk. The equations are arranged in a grid-like pattern and the formulas appear to be related to solving a mathematical problem. The man is looking down at the board with a focused expression on his face.</caption><caption><image_48>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 board with a marker. The board is filled with mathematical equations and formulas written in white chalk. The equations are written in a neat and organized manner, and the formulas are clearly visible. The man seems to be focused on the task at hand.</caption></video><transcript><audio_49> vezes 2 elevado a 3. Pelo teorema de Fermat, 2 elevado a 18 é congruente a 1, módulo 19. Então, esse bloco todo vira 1 e isso aqui vai dar 8. Portanto, 8 é a classe de</transcript><caption><image_50>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt and appears to be a teacher or a student. The chalkboard is filled with mathematical equations and formulas written in white chalk. The equations are written in a neat and organized manner, and the formulas appear to be related to algebra. The man is pointing to one of the equations with his right hand, as if he is explaining them to the viewer.</caption><transcript><audio_51> Aqui você vê um resumo das informações que nós obtivemos na primeira etapa da nossa solução. A segunda etapa da nossa solução consiste em</transcript><caption><image_52>The image shows a man standing in front of a green chalkboard with mathematical equations written on it. He is wearing a black t-shirt and appears to be in the middle of a lesson or presentation. The equations are written in white chalk and are arranged in a grid-like pattern. The man is standing with his hands on his hips and is looking up at the equations with a focused expression on his face. The background of the image is blurred, but it seems to be a classroom or a classroom setting.</caption><transcript><audio_53> de congruências, que têm exatamente os mesmos números, 1, 7 e 8, respectivamente com os mesmos módulos, 7, 11 e 19.</transcript><video><caption><image_54>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt and appears to be a teacher or a student. The man is pointing to a mathematical equation written on the chalkboard with his right hand. The equation is written in white chalk and is written on a blackboard. The background of the image is a plain green wall.</caption><caption><image_55>The image shows a man standing in front of a green chalkboard with mathematical equations written on it. He is wearing a black t-shirt and appears to be in the middle of a math lesson. The equations are written in white chalk and are arranged in a grid-like pattern. The man is pointing to one of the equations with his right hand, as if he is explaining them to the viewer. He has a serious expression on his face and is gesturing with his left hand. The background of the image is blurred, so the focus is on the man and the chalkboard.</caption><caption><image_56>The image shows a man standing in front of a green chalkboard. He is wearing a black t-shirt and appears to be a teacher or a student. The chalkboard is filled with mathematical equations and formulas written in white chalk. The man is pointing towards one of the equations with his right hand, as if he is explaining something. The equations are written in a neat and organized manner, and the formulas appear to be related to mathematics. The image appears to have been taken in a classroom or a classroom setting.</caption></video><transcript><audio_57> nos permite afirmar que esse sistema tem solução única módulo 7 vezes 11 vezes 19 que é 1463 eu posso afirmar isso porque 7 ou</transcript><caption><image_58>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 a teacher or a student. The man is pointing to a mathematical equation written on the chalkboard with his right hand. The equation is written in white chalk and is surrounded by other mathematical equations and formulas. The background of the image is a plain green wall.</caption> 144 4 number as follows  2 raised to 18 which in turn is raised to 18 x 2 raised to 3 by Fermar's theorem 2 raised to 18 is congruent to 1 module 19 So this whole block becomes one and this here will give o8 therefore 8 is the equivalence class  of our power of 2 module 19 Here you see a summary of the information that we obtained in the first step of our solution the second step of our solution consists of looking at this system of congruences that has exactly the same numbers 1 7 and 8 respectively with the  same modules 7 11 and 19 the Chinese remainder theorem allows us to state that this system has a unique solution module 7 x 11 x 19 which is 1463 I can say this because 7 11 and
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