2003 Volume 44 Issue 1-2 Pages 51-60
:It is known that for the positive integers a, bw hich are coprime to each other an integer n satisfying n ≥ (a -1) (b -1) can be expressed in the form ax+ by, x, y being non-negative integers. In this paper, we investigate this property in the special cases a= 2, b = 3 and a= 3, b = 4, 5. For the proposition above, G. Polya used a distribution table of numbers. We express these numbers as the products of matrix and vector matrix, and consider some properties by using lattice points in the coordinates plane from the algebraic and geometric viewpoints. We believe that it is important to consider why some numbers can not be expressed as ax+ by from these viewpoints. We consider the teaching materials relating to the property stated above at the level of high school mathematics. This paper is also a case study of the problem solving.
