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The square body - the numerical body of degree 2 extending over the body of rational numbers. Square bodies are the simplest non-trivial numbers, and were the first to be studied historically, which laid the foundations for modern algebraic number theory. To this day, square bodies are an inexhaustible source of interesting and difficult mathematical problems and have extremely important practical applications in numerical theory. Example

An example of a square body is a set of numbers a + b 2 {\displaystyle a+b{\sqrt {2}}} where a and b are rational numbers, and simple addition and multiplication.

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