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ON REPRESENTATION OF AN INTEGER BY X 2 + Y 2 + Z 2 AND THE MODULAR EQUATIONS OF DEGREE 3 AND 5.

By Alexander Berkovich

Abstract

There are always flowers for those who want to see them Abstract. I discuss a variety of results involving s(n), the number of representations of n as a sum of three squares. One of my objectives is to reveal numerous interesting connections between the properties of this function and certain modular equations of degree 3 and 5. In particular, I show that n s(25n) = (6 − (−n|5)) s(n) − 5

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