TOPICS
Search

Ford's Theorem

Let a, b, and k be integers with k>=1. For j=0, 1, 2, let

S_j=sum_(i=j (mod 3))(-1)^i(k; i)a^(k-i)b^i.

Then

2(a^2+ab+b^2)^(2k)=(S_0-S_1)^4+(S_1-S_2)^4+(S_2-S_0)^4.

See also

Bhargava's Theorem, Diophantine Equation--4th Powers

Explore with Wolfram|Alpha

References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 100-101, 1994.

Referenced on Wolfram|Alpha

Ford's Theorem

Cite this as:

Weisstein, Eric W. "Ford's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FordsTheorem.html

Subject classifications