Representing Integers as Sums of Squares
نویسنده
چکیده
We study in detail the special case of Waring’s problem when the power k = 2. Ultimately, we prove that four is the least number of squares needed to represent any integer. To this end, we prove that some numbers cannot be represented as sums of two squares, some cannot be represented as sums of three, and all can be represented as sums of four. We also show that numbers of a certain form can be represented as sums of two squares. Though we mostly use classic methods of number theory, we venture into group theory to prove a few preliminary theorems.
منابع مشابه
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تاریخ انتشار 2009