APPLICATION OF SOME METHODS OF NUMBER THEORY IN THE PROCESS OF SOLVING SCHOOL PROBLEMS ON DIVISION OF WHOLE NUMBERS

Abstract

Using the language and properties of numerical comparisons a number of tasks from number theory are solved in the article. It turns out that the use of comparisons in problems is a very convenient and very powerful tool, because, as we will see later, it allows us to work with additions in the same way that, according to the habit, we can work with equalities, that is, addition, subtraction, multiplication , sometimes divide them.  The present article examines the solution of division problems by methods that demonstrate the use of summation theory, consideration of remainders, and Euler's theorem. The first and third methods are new for public school teachers, probably, and the second method is convenient to use, in the event that the divisor is not a very large number. The work consists of three paragraphs. Each paragraph contains a theoretical part and examples of solving problems. Particular attention is paid to the list of used literature [1-8], it contains the best textbooks of elementary number theory. Most of the exercises in the manual are taken from those books.