We generalize a theorem of Birch on solving systems of homogeneous equations of odd degree to the case of solving systems of homogeneous equations of degree not divisible by a fixed integer s ≥ 2. Birch's theorem is the case s = 2. In addition, we give a new exposition of the proof of Brauer's theorem on solving systems of homogeneous equations.
|Number of pages||9|
|Journal||Communications in Algebra|
|State||Published - Aug 2009|
- Birch's theorem
- Systems of homogeneous equations
ASJC Scopus subject areas
- Algebra and Number Theory