What is the sum of the 3rd cube number and the 5th cube number?
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Let n be a whole number. When is it possible to write n as a sum of two squares, say n=a2+b2, or as a sum of three squares, say n=a2+b2+c2, or as a sum of four squares, and so on? Of course, a, b, c, … are also meant to be whole numbers here. We can also ask whether there is any convenient test to decide whether n is the sum of one square; that is, whether n is itself a square number, say n=a2. In this article we shall mention some of the interesting answers to these questions. The proofs, which belong to the subject called Number Theory, are too difficult to be given here, but take a look at the article written by Tom Sanders, aged 16.
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the sum of the 3rd cube number and the 5th cube number is 3152
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