When arithmetic has accumulated a wealth of solutions to quantitative problems, in order to find a more systematic and universal method to solve various quantitative relations problems, elementary algebra with the solution of equations as the center problem has emerged. So that for a long time, mathematicians have understood algebra as the science of equations and focused on the study of equations. That is to say, the theory and method of algebraic operation of numbers and words, more precisely, the theory and method of algebraic operation of polynomials, and its research method is computational.
After number theory became an independent discipline, with the development of various branches of mathematics, new methods of studying number theory appeared. According to the research methods, number theory can be divided into elementary number theory, analytic number theory, algebraic number theory and geometric number theory.
To discuss the equation, first of all, how to express the actual quantitative relationship as algebraic expression, and list the equation according to the equivalence relationship. Algebraic expressions include algebraic expressions, fractions and roots. Algebraic expressions can perform four operations of addition, subtraction, multiplication and division, as well as multiplication and square root operations, and abide by the basic operational rules.
Elementary number theory does not rely on other mathematical disciplines, but only relies on elementary methods to study the properties of integers.
In the development of solving equation problems, the number system has been expanded. The concepts of integers and fractions discussed in arithmetic are extended to the scope of rational numbers, so elementary algebra can solve more problems. However, there are still some equations that have no solutions within the rational number range. Thus, the concept of number is once again extended to real numbers and further extended to complex numbers.