The b-adic representation is a way of representing a non-negative integer using a base b. It involves expressing the integer as a sum of multiples of powers of b. For example, in base 10, the number 365 can be represented as 3*10^2 + 6*10^1 + 5*10^0. This representation allows for easy conversion between different bases and is commonly used in computer science and number theory. **

To multiply 7-adic numbers, you can use the same method as multiplying regular integers, but with carrying out the operations modulo 7 at each step. Start by multiplying the corresponding digits of the two numbers, then carry over any excess to the next digit. Repeat this process for each digit position. Remember that in the 7-adic number system, each digit can only be between 0 and 6. **

A b-adic fraction is a way of representing a real number using a base b expansion. It is similar to a decimal expansion, but instead of using base 10, it uses base b. The b-adic expansion of a number consists of a sequence of digits, each of which represents a multiple of a power of b. The expansion can be finite or infinite, and it can be used to represent both rational and irrational numbers. **

To convert recurring fractions into q-adic representation, we can use the formula for converting a recurring fraction to a q-adic number. First, we express the recurring fraction as a continued fraction. Then, we use the formula for converting a continued fraction to a q-adic number, which involves finding the convergents of the continued fraction and expressing them in terms of powers of q. This process allows us to represent the recurring fraction as a q-adic number. **

Streaming movies from the cinema without proper authorization is illegal. This is because it violates copyright laws and intellectual property rights. The movies shown in cinemas are the property of the filmmakers and production companies, and streaming them without permission is a form of piracy. It is important to respect the rights of content creators and support the legal distribution of movies. **

Yes, black and white films are often used in the background of Hollywood movies to add authenticity to a scene or to create a specific mood. These classic films are sometimes shown on television screens or in movie theaters within the movie to enhance the setting or time period. Additionally, black and white films are sometimes used as a stylistic choice by directors to evoke a sense of nostalgia or to pay homage to the history of cinema. **

The answer to whether movies or TV series are better ultimately depends on personal preference. Movies typically offer a more condensed and focused storytelling experience, while TV series allow for more in-depth character development and complex story arcs over multiple episodes. Some people may prefer the convenience of watching a movie in one sitting, while others enjoy the anticipation and ongoing engagement of following a TV series over time. Both mediums have their own unique strengths and can provide enjoyable entertainment experiences. **

Yes, streaming paid movies and series on free streaming sites in Austria is illegal. These sites often host copyrighted content without permission, which violates intellectual property laws. Engaging in this activity can result in legal consequences, including fines or other penalties. It is important to use legal and authorized streaming services to access movies and series in Austria. **