Five squares in arithmetic progression over quadratic fields

Details Five squares in arithmetic progression over quadratic fields Five squares in arithmetic progression over quadratic fields

2009-09-09

arxiv.org/abs/0909.1663v3

Mathematics

Number Theory

Scientific paper

We give several criteria to show over which quadratic number fields Q(sqrt{D}) there should exists a non-constant arithmetic progressions of five squares. This is done by translating the problem to determining when some genus five curves C_D defined over Q have rational points, and then using a Mordell-Weil sieve argument among others. Using a elliptic Chabauty-like method, we prove that the only non-constant arithmetic progressions of five squares over Q(sqrt{409}), up to equivalence, is 7^2, 13^2, 17^2, 409, 23^2. Furthermore, we give an algorithm that allow to construct all the non-constant arithmetic progressions of five squares over all quadratic fields. Finally, we state several problems and conjectures related to this problem.

Affiliated with

Also associated with

No associations

Rating

Five squares in arithmetic progression over quadratic fields 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 Five squares in arithmetic progression over quadratic fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Five squares in arithmetic progression over quadratic fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-385869