Bhargava's Theorem
Let the 
th composition of a function 
be denoted 
, such that 
and 
.Denote 
, and define
 | (1) |
 |  |  | (2) |
 | |  | (3) |
 | |  | (4) |
and
 |  |  | (5) |
|  | (6) | |
 | |  | |
|  | (7) |
Then if
, | |  | |
|  | (8) |
where
and composition is done in terms of components.See also Diophantine Equation--Quartic, Ford's Theorem
References
Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 97-100, 1994. Bhargava, S. ``On a Family of Ramanujan's Formulas for Sums of Fourth Powers.'' Ganita 43, 63-67, 1992.
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