Symmetric homogeneous diophantine equations of odd degree

Details Symmetric homogeneous diophantine equations of odd degree Symmetric homogeneous diophantine equations of odd degree

2008-09-23

arxiv.org/abs/0809.3973v2

Mathematics

Number Theory

Scientific paper

We find a parametric solution of an arbitrary symmetric homogeneous diophantine equation of 5th degree in 6 variables using two primitive solutions. We then generalize this approach to symmetric forms of any odd degree by proving the following results. (1) Every symmetric form of odd degree $n\ge 5$ in $6 \cdot 2^{n-5}$ variables has a rational parametric solution depending on $2n-8$ parameters. (2) Let $F(x_1, ..., x_N)$ be a symmetric form of odd degree $n\ge 5$ in $N=6 \cdot 2^{n-4}$ variables, and let $q$ be any rational number. Then the equation $F(x_i)=q$ has a rational parametric solution depending on $2n-6$ parameters. The latter result can be viewed as a solution of a problem of Waring type for this class of forms.

Affiliated with

Also associated with

No associations

Rating

Symmetric homogeneous diophantine equations of odd degree does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symmetric homogeneous diophantine equations of odd degree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symmetric homogeneous diophantine equations of odd degree will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-327702