Abstract
This chapter discusses elementary problems in arithmetic. The unsolved problems of arithmetic can be classified into two kinds. The problems of the first kind are problems for which it is known how to obtain the complete solution, and the only difficulty is that it is not possible to perform all the necessary computations, because of their length, even with the assistance of the biggest calculating machines that exist at present. This difficulty is, therefore, purely technical. All other unsolved problems are classified as problems of the second kind. As regards each of these problems, no method is known that could lead to a solution, even after extremely long and most tiresome calculations that possibly exceed human capabilities of today. A problem of the first kind is to find all the natural divisors of 2101−1. A problem of the second kind is the question whether the equation x3 + y3 + z3 = 3 has integral solutions x, y, z other than the four known solutions.
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