Ramanujan,s Sum
المؤلف:
Hardy, G. H.
المصدر:
Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea
الجزء والصفحة:
...
24-8-2020
1212
Ramanujan's Sum
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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