Authors: Zhang Tianshu
In this article, we classify positive integers step by step, and use the formulation to represent a certain class therein until all classes. First, divide all integers ≥2 into 8 kinds, and formulate each of 7 kinds therein into a sum of 3 unit fractions. For the unsolved kind, again divide it into 3 genera, and formulate each of 2 genera therein into a sum of 3 unit fractions. For the unsolved genus, further divide it into 5 sorts, and formulate each of 3 sorts therein into a sum of 3 unit fractions. For two unsolved sorts i.e. 4/(49+120c) and 4/(121+120c) where c≥0, we use an unit fraction plus a proper fraction to replace each of them, then take out the unit fraction as 1/x. After that, we take out an unit fraction from the proper fraction and regard the unit fraction as 1/y, and finally, prove that the remainder can be identically converted to 1/z.
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