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Date: 24-12-2020
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The sum
(1) |
where runs through the residues relatively prime to , which is important in the representation of numbers by the sums of squares. If (i.e., and ' are relatively prime), then
(2) |
For argument 1,
(3) |
where is the Möbius function. For general ,
(4) |
where is the totient function.
REFERENCES:
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, pp. 137-143, 1999.
Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, p. 254, 1991.
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